Smack in the Middle (2) - S1-E2
Deliberate mistake: Ignoring that its very unlikely all of Jill St. John's copious red hair would fit under a wig that passes for Robin's hair, it's impossible that it would emerge from under that wig looking as full and perfectly styled as it does when she's in the Batcave.
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