The Bird's Last Jest (2) - S2-E28
Visible crew/equipment: Batman tilts the Bat Shield just a little too much when he and Robin are under fire from Penguin's goons, and it captures a pretty clear reflection of the camera rigging. (00:04:00)
Penguin Sets a Trend (2) - S2-E43
Visible crew/equipment: The Batmobile, responding to Batman's remote control activator, is supposedly driving itself through Gotham City's streets. But in one shot, even though he's crouching down, you can see the head of the film crew member actually driving the car. (00:03:00)
It's the Way You Play the Game (2) - S2-E26
Visible crew/equipment: After Batman gets out of the Batmobile, you can see the lighting rigs, boom mic, camera and crew reflected on the Batmobile's side.
Caught in the Spider's Den (2) - S2-E56
Visible crew/equipment: When Batman and Robin are caught in Black Widow's web, the wires used to operate the spiders are visible.
A Riddling Controversy (2) - S2-E46
Visible crew/equipment: During the "Batfight" at the end, it is extremely obvious that the Riddler is a stuntman and not John Astin, note that the stuntman does not have a mustache.
The Penguin's a Jinx (2) - S1-E4
Visible crew/equipment: As Mr. Jay is talking to Bruce and Dick, on the wall behind Dick you can see the shadow of the boom mic. (00:23:45)
Penguin's Disastrous End (3) - S2-E44
Visible crew/equipment: As O'Hara goes to move his patrol car, the boom mic and lighting equipment is reflected on the windows.
Visible crew/equipment: When the photographer is getting a picture of the princess, you can see the shadow of the boom mic on him.
The Thirteenth Hat (1) - S1-E13
Visible crew/equipment: As Gordon goes to the Batphone to alert Batman, the shadow of the camera covers most of him for about a full three to four seconds.






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