The Thirteenth Hat (1) - S1-E13
Visible crew/equipment: When Hatter is at Octave Marbot's studio posing as him, Batman and Robin arrive, and chalk T-marks are visible on the floor near Batman's statue in the studio. Then while Batman is in the dressing room, Hatter quietly opens the studio's front door, and more chalk T-marks are visible on the floor in the hall. (00:18:40)
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