Catwoman Goes to College (1) - S2-E49
Continuity mistake: When they first go to the bat poles, Bruce is on the right. The next shot at the bottom, Bruce/Batman is on the left and Dick/Robin is on the left. They switched sides. It has happened throughout the series.
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