In Season 1, Rick travels to Atlanta, and the rest of the survivors later travel to the CDC headquarters. Why, after 4 seasons (with the exception of Eugene and Abraham), has the show not suggested/explored the possibility of traveling to another major city? It would seem rural Georgia might be preferable from the standpoint that the relative density of walkers to humans is likely to be less away from a major city, but also less preferable in terms of actually finding supplies, other survivors, state supported aid, or questions as to what caused the outbreak. While the show seems to be more about what happens to the survivors, and less about whatever caused the apocalypse, eliminating the characters' interest in exploring how the disease has affected other parts of the country doesn't completely make sense.
It would be a very dangerous journey, requiring the expenditure of vast amounts of resources for something which does not have a defined objective.
It is difficult to drive to and through cities due to the roads being blocked by broken down cars, herds of walkers, general rubble etc. Walking would be very dangerous as there are natural hazards, walkers, hostile humans etc.
If they managed to find another city they would potentially be set upon by herds of walkers, in unfamiliar terrain with only the resources they could carry.
If they managed to survive the walkers then they might or might not find other survivors who might or might not be friendly.
It is a far better use of resources to fortify where they are and try to survive. I am sure they are curious as to what is happening elsewhere but to attempt to travel there would be quite out of character and, tbh, almost suicidal.
TL;DR: They have.
On the Show:
Rick rides into Atlanta alone, where he meets Glenn, T-Dog, Jacqui, Morales, Merle, and Andrea.
The group later returns to Atlanta to rescue Beth from Grady Memorial Hospital.
They soon hear about a group of survivors in Virginia, and decide to join them.
The sign in this scene says:
Fort Myers: 10
Along the way, they pass Washington, DC.
They finally reach the community of friendly survivors in Alexandria, Virginia.
Alexandria is literally just across the Potomac River from Washington.
Amy and Andrea were from Florida; also overrun.
In the Comics:
The characters start out at an unknown campsite on the outskirts of Atlanta, the biggest city in Georgia.
Rick is from Cynthiana, Kentucky - a real place which is also the hometown of the creator of The Walking Dead, Robert Kirkman.
Rick wakes up from his coma in Harrison Memorial Hospital in Cynthiana.
He rides into Atlanta along an empty highway.
There, he meets Glenn.
They eventually head for Washington D.C.
And finally discover the Alexandria Safe Zone in Alexandria, Virginia, which is just across the Potomac from Washington.
They are clearly no longer in a rural area by any definition of the phrase.
They make allies in the Kingdom, which appears to be located in Washington, DC.
Specifically, the Kingdom's headquarters seems to be Eastern Senior High School.
In addition to the places seen, and places of origin of the TV characters, the comics feature characters from or in:
Why haven't they tried to reach other cities?
It will be a dangerous trip
The trip will eat up valuable resources
In the real world "city" means "place with tons of people"; in the Walking Dead world, "city" means "place with lots of zombies".
Issue #10 of the comics says that zombies outnumber humans by a ratio of 5,000:1. This means that a group traveling through the US will be facing 299,940,000 zombies.
So they'd be expending resources and facing a perilous journey, despite knowing that reaching their destination will not benefit them in any way, and when they get there, they'll be surrounded by hundreds of thousands/millions of zombies.
What we've seen:
On the shows:
The Walking Dead:
The last time anyone heard from the government, they were being told to head for the major cities.
Duane: They [Rick's family] are in Atlanta, I'll bet.
Morgan: That's right.
Rick: Why there?
Morgan: Refugee center. Huge one, they said, before the broadcasts stopped. Military protection, food, shelter... They told people to go there. Said it'd be safest.
- The Walking Dead, S1E1, Days Gone Bye
When Shane was stuck on the road into Atlanta with Lori, trying to reach the refugee center, the emergency broadcasts telling people to go there suddenly cut off:
Lori: You getting anything?
Shane: There's nothing.
Lori: Big surprise there.
Shane: No, I mean there's nothing. Emergency broadcast system stopped, and that recording about the refugee center. It's all gone. I'm gonna go up the road, see what I can see.
- The Walking Dead, S2E5, Chupacabra
What he and Lori see when they go up the road isn't very reassuring:
As Shane says:
They're dropping napalm in the streets!
It stands to reason that this happened in every major city - everyone heard the emergency broadcasts telling people to head for the big cities, those cities were quickly overrun by zombies, and one of the military's last acts before communications broke down was to firebomb them.
Later, the group reaches the Centers for Disease Control building in Atlanta, where they get more bad news:
Rick: Where is everybody? The other doctors, the staff?
Dr. Jenner: I'm it. It's just me here... I'm all that's left.
- The Walking Dead, S1E6, TS-19
Later, the news gets worse:
Dr. Jenner: It was the French.
Dr. Jenner: They were the last ones to hold out as far as I know. While our people were bolting out the doors and committing suicide in the hallways, they stayed in the labs till the end. They thought they were close to a solution.
Jacqui: What happened?
Dr. Jenner: The same thing that's happening here. No power grid. Ran out of juice.
- The Walking Dead, S1E6, TS-19
The infection is not limited to Atlanta, or even the US - it has destroyed the entire world.
Dr. Jenner: There is no hope. There never was.
Rick: There's always hope. Maybe it won't be you, maybe not here, but somebody somewhere...
Andrea: What part of "everything is gone" do you not understand?
Dr. Jenner: Listen to your friend. She gets it. This is what takes us down. This is our extinction event.
- The Walking Dead, S1E6, TS-19
In season two, the group meets a pair of guys from up north, and finds out what they already knew: nowhere is safe.
Dave: We met on I-95 coming out of Philly [Philadelphia, Pennsylvania].
Tony: Damn shit-show that was. [i.e., Philadelphia and its environs (including NYC) are gone]
Rick: Well, what drove you South?
Dave: Well, I can tell you it wasn't the weather. I must've dropped 30 lbs. In sweat alone down here.
Tony: I wish.
Dave: No, first it was D.C. I heard there might be some kind of refugee camp, but the roads were so jammed, we never even got close. We decided to get off the highways, into the sticks, keep hauling ass. Every group we came across had a new rumor about a way out of this thing.
Tony: One guy told us there was a Coast Guard center in the Gulf, sending ferries to the islands.
Dave: The latest was a rail yard in Montgomery [Alabama] running trains to the middle of the country... Kansas, Nebraska.
Tony: Low population, lots of guns.
Glenn: Kinda makes sense.
Dave: Ever been to Nebraska, kid? A reason they call 'em flyover states... How about you guys?
Rick: Fort Benning [Georgia], eventually.
Dave: I hate to piss in your cornflakes, officer, but... We ran across a grunt who was stationed at Benning. He said the place was overrun by lamebrains [i.e., zombies].
Glenn: Wait, Fort Benning is gone? Are you for real?
Dave: Sadly, I am. Ugly truth is, there is no way out of this mess. Just keep going from one pipe dream to the next, praying one of these mindless freaks doesn't grab a hold of you when you sleep.
Tony: If you sleep.
- The Walking Dead, S2E8, Nebraska
Fear the Walking Dead:
Los Angeles was overrun and firebombed in S2E1, Monster.
They get on a yacht and head for San Diego, but...
Travis: Nick found a logbook to that boat. We got a problem. San Diego's dead.
Daniel: How bad?
Madison: It's gone.
Strand: What? Wait, wait, wait.
Daniel: What do you mean gone?
Madison: It's burned. The military burned it down. According to this, the Leigh Anne just came from the south right there.
- Fear the Walking Dead, S2E2, We All Fall Down
Later in the same episode, a park ranger gives them more bad news:
George: You folks are from Los Angeles. You got that air about you.
Travis: We left when they started bombing.
George: Napalm. It's what they're using up and down the coast. I've been checking in with some of the other ranger stations.
Travis: It's in every city?
George: As far as I can tell. Portland, Seattle, Vancouver.
Travis: And south?
George: San Diego was burned.
Travis: (sighs) Further south?
George: They shut down the border. No way in or out.
Travis: Oh, God. So what's left?
George: Not a hell of a lot. Interior is no better than the coast. Last time I connected to Joshua Tree [California], ranger said Petrified Forest [Arizona], gone. JT shut down soon after. That's Cali, that's Arizona. Zion [Utah] went dark before them. Utah gone. Rocky Mountain station [Colorado] is dead. That's Colorado. That's the Continental Divide. That's a good goddamn half the country.
- Fear the Walking Dead, S2E2, We All Fall Down
The tie-in miniseries, Fear the Walking Dead: Flight 462 shows Phoenix, Arizona going dark.
They check out Catalina Island, CA:
They reach Baja, Mexico:
And end up in El Rosarito:
In the Comics:
We know that everywhere the group has been - from Kentucky to Atlanta to rural Georgia and north into Virginia and Maryland - has been completely devastated by the outbreak. We also know that Abe is from Houston, Rosita is from Dallas, and both were destroyed.
Between Macon and Savannah
All full of zombies.
Kenny came from Fort Lauderdale, Florida.
Christa and Omid were from San Francisco, California, and were in Las Vegas, Nevada when the apocalypse began.
Places mentioned as being destroyed, either explicitly or by implication:
Basically, everywhere else in Georgia
New York, NY
Blue Mountains, VA
Basically, the rest of Virginia
Parker's Crossroads, Tennessee
The rest of Tennessee
Fort Lauderdale, FL
Las Vegas, NV
Los Angeles, CA
San Francisco, CA
San Diego, CA
Joshua Tree, CA
Catalina Island, CA
The rest of California
Zion National Park, Utah
The rest of Utah
Rocky Mountain National Park, CO
The rest of Colorado
Petrified Forest, AZ
The rest of Arizona
Vancouver, BC, Canada
Looking for supplies in places they haven't been:
On the show, about two years have passed. In the comics, it is closer to five years. There isn't much left to scavenge, and what is left has begun to rot. Canned food is usually given a two-year expiration date. Although the expiration date on a can has nothing to do with food safety, and canned food will be safe to eat as long as the can remains intact and undamaged, intact and undamaged cans will become harder to find as buildings deteriorate and the cans inside them are exposed to the elements.
Trying to find out more about the pathogen that caused the outbreak:
This simply isn't useful information for the survivors. They know zombies are dangerous, they know how to kill them, and they know everyone is infected but the infection isn't lethal. Knowing how it started and what kind of pathogen it is might be interesting, but it won't help anyone. They are much more concerned about staying alive than studying epidemiology. The information just isn't important to them.
The people in the Walking Dead universe have actually traveled quite a bit, seen many cities, and heard news of many others. All of their experience has taught them that there simply isn't anywhere to go.
19 states in the US are known to be infected, and presumably totally wiped out, as well as places in three other countries - British Columbia, Canada; Baja, Mexico; and Catalonia, Spain; the entire country of France is said to be destroyed as well.
However, the fact that the infection is known to be spread across five countries on two continents suggests that we can safely assume far more than this. By all appearances, the entire world is in the same condition as rural Georgia.
The park ranger on FTWD says "half the country" [i.e., everything west of the Rocky Mountains] is gone; we know that the eastern seaboard from Florida to New York, and many landlocked states in the eastern US, are no better off than the western US. Canada, Mexico, Spain, and France are overrun. Jenner at the CDC says the French came closest to understanding the pathogen that caused the outbreak, which implies that there were many other countries which fell before they made similar progress.
And most telling of all, Dr. Jenner says Andrea "gets it" when she reminds Rick that "everything is gone". "Everything" obviously means "the world".
Why don't the survivors try to go elsewhere? In short, because there's absolutely no point.
Accompanying map (Only approximate locations.)
At the start of the outbreak people was told to go to the cities where the army could keep watch. Rick himself, after his wakeup and biking around the hometown, leaves for Atlanta as that is the place most plausible his family has gone.
After his meetup with the family outside the city and their escapades they set course for CDC, which is placed inside Druid Hills, Georgia, just outside the city. As that ends in a big bang the plan is to travel south to Fort Benning, near Columbus. This is also the introduction to season two as Rick have his morning broadcast to Morgan on his walkie-talkie.
On their way they get stuck in the jam on the road and ends up on Hershel's farm.
After Rick learn of his wife's pregnancy and as people settles in on the farm the intentions is split, but more and more pointing to trying to stay at the farm. It is good as any, and with a pregnancy to think about, the need of someone with medical expertise is critical. Especially since it is likely to be a C-section.
Hershel finds his old friend, (the hip flask), after the massacre of his walker family and finally ends up at Hatlin's Bar. Rick and Glenn follows him and they all meet Dave and Tony. Though these are shady people the information they give is likely true as any.
They met up on i95 out of Philadelphia trying to get to Washington DC, but as the roads was all jammed up they went off the highways and headed south. One pipe dream to the next.
They further tells that each new group they meet have a new rumor. Some say ferries goes out from the Gulf to the islands, and the latest was a rail yard in Montgomery where trains goes to Kansas / Nebraska.
Most important they say Fort Benning has fallen. After this the fort is not mentioned until we meet the camp of former Philip Blake's (AKA The Governor, Brian Heriot) lieutenant Caesar Martinez. Here we meet Pete Dolgen which was positioned at Fort Benning when the outbreak occurred.
After the farm is overrun they travel from place to place. Close to 8 months? It is not easy to have any set goal, other then finding a safe place. It is likely they have the same experience as told by Dave and Tony. Rumors and new rumors. Bad people, bad walkers, etc. We also witness Carl's attempt to share a meal of dog-food with the group, though adverted by Rick, it tells the level of needs for resources. That owl is also not exactly chicken. As such when they eventually come across the prison that is as good a place as any.
One important factor for their prolonged stay at the prison is also Rick's meltdown after Lori dies, and just as important when he realizes what the life thus far has done to Carl. He is close to be a sociopath. As such it becomes very important for him to bring Carl back to a life where it is not all about kill or be killed. Turning back out on the road would become such an endeavor.
Further they accept the people form Woodbury among which we find both elders and children. Not the gang you would want to take on a cross country tour.
We also meet the soldiers that were mowed down by The Governor and his men. They were out scouting and they was lost as any. Further the despair and what is out there is underlined by the meeting with Clara at the start of season 4. Tragic and extreme as it was, it was likely not unique.
It has been suggested in several episodes that the answers lie in other parts of the country, and it has also been suggested that they're all lies. I can't remember the episode but one of the characters, when talking about safe-havens, says something like, "On the east coast they say it's the west coast, on the west coast they say it's the east coast..." I think they're pretty much in "Survival" mode at this point, and just looking for another place like the prison where they can dig in and make a community.
As I recall, one of the secondary characters for the past few episodes was a doctor or scientist who needed to get to DC because he has the supposed cure. So, at least in other characters they come across, people are trying to get to, or have gone to, other locations in the country.
But I'm sure one of the biggest factors is also the generous tax credit given to productions filmed in Georgia which display the Georgia Entertainment logo in the credits.