OK, so Bruce had his very own Batcave installed on Arkham Island, because basically he "anticipated" the events that happened in the last game going down. But where's he gonna hide it this time? Wayne Manor is several miles outside of Gotham...
REAL Campers Camp with a Purpose. REAL Campers Camp for the Team.
Extreme is correct, Batman has several Satellite Bat Caves around Gotham, for example the one beneath Robinson Park. It's discussed in the "No Man's Land" arc and others. Not to mention there are several facilities hidden in Wayne tower that are used by Batman when travel back to the Bat Cave is inefficient or not possible. Also as depicted in Nightwing, Bruce has several safe houses set up within Gotham, no doubt they would be equipped with holdout supplies and facilities, and a secure network link to the main Bat Computer @ Wayne Manor.