Antonio's Fortress, built by Herod the Great. It is located on the Northern wall of the Temple Mount and it housed the Roman Garrison stationed at Jerusalem. The South wall of the Fortress would allow the guard to look right over into the Temple mount area. This is where Paul would have been taken when rescued from the mob by the Roman guard.
A Photo of model of buildings in Jerusalem. The monument with the pyramidal top is the first-century Tomb of David (alluded to by Peter in Acts 2:29), not the actual burial site which on Ophel hill to the east. Identification by Chris Bullard.