Where do I find the Batcave in Arkham City?
The Batcave is not available through regular gameplay because Wayne Manor is not located inside the Arkham City area. However, you can play it as a challenge map in one of the DLC.
Source
The Batcave is not available through regular gameplay because Wayne Manor is not located inside the Arkham City area. However, you can play it as a challenge map in one of the DLC.
Source