The Bookworm Turns (1) - S1-E29
Revealing mistake: At about the 6:40 mark into the episode, The Bookworm puts an explosive device in the Batmobile which is detected automatically. Batman pushes the auto eject to throw it out of the car. As the special effects prop explodes, you can see the rope it is hanging from as it swings to the side.
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