The Joker's Provokers (2) - S2-E22
Revealing mistake: When Alfred talks to his twin Egbert, as they face each other, you can plainly see the line dividing the screen so that Alan Napier can play both parts.
An Egg Grows in Gotham (1) - S2-E13
Revealing mistake: A lot of the time, especially in close ups, you can see the line between the bald dome wig and Vincent Price's real skin, as well as the different coloring of skin.
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