In several crossovers, the characters from both series go back and forth between these two cities. In a scene, Oliver was on a motorcycle.
What is the distance between these two cities?
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You can see more details in my vain and failed attempt to figure out where the heck Starling City is. However, there were a few scenes where characters estimate that it's about 600 miles between the two cities. For example, at the end of The Flash's pilot episode, we get:
Oliver Queen: So why come to me? Something tells me you didn't just run 600 miles to say hi to a friend.
This means that normal characters would need at least 10-12 hours to get from one place to another, though Barry can obviously get there about a half hour at top speeds (~Mach 2).
This is born out a bit in the most recent cross-over, "Legends of Today" / "Legends of Yesterday". When the combined Team Arrow and Team Flash members realize they need to get from Starling City to Central City very quickly, they end up taking Felicity's private jet. These kinds of planes typically travel in the 400mph to 600mph range, so it wouldn't make sense to take one if your cities weren't at least several hundred miles apart.
It's a bit hard to pin down because the assumed or affirmed locations of cities have changed over time.
However, according to the wiki for the "Arrowverse" shows, Central City is located approximately 600 miles from Star City. The citation for the number is apparently derived from the pilot episode of The Flash.