The Entrancing Dr. Cassandra - S3-E25
Continuity mistake: The Batmobile returns to the Batcave by remote control. It's facing left when we get a brief, three-second shot of Batgirl talking to Batman and Robin. In the very next shot, the Batmobile has instantly turned itself around and is facing right. Its turntable (which was actually pushed manually by stagehands under the platform) didn't work quite that fast. (00:18:05)
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