Flop Goes the Joker (2) - S2-E58
Revealing mistake: At the "Batfight", the Joker leaves the room and he kidnaps Baby Jane but when it cuts back to the fight, if you look closely at the door, the Joker can be seen leaving the room again. Note his iconic pink suit.
Flop Goes the Joker (2) - S2-E58
Revealing mistake: After Bruce stops the governor of the mobile, it can be seen that the weights are painted Styrofoam balls.
Answer: There wasn't one singular city used. It was shot in and around various locations in California, plus on a lot of sets and backlots. Ex. Some scenes were shot in LA, some in Pasadena, some in Santa Barbara, etc.
TedStixon