Batman's home turf, Gotham City, has been DC Comic's analogy for New York since its creation. The city's geography and even the gentrification it experienced over the course of the comic's history, have both been reflected in Gotham City. The city has always been a hot-bed of crime, despite Batman's many years of service.
The main setting in the game which consists of two areas: Old Gotham and New Gotham.
Arkham City is actually Old Gotham which has a giant prison wall.