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.
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.