Batman Sets the Pace (2) - S1-E26
Visible crew/equipment: When Alfred whispers to Bruce about the Batphone, the boom mic is visible over Alfred at the top of the screen. (00:23:20)
True or False-Face (1) - S1-E17
Visible crew/equipment: After Albert answers the Batphone it cuts to Bruce and Dick sitting at the table. We can see a chalk T-mark on the floor near Dick, and a white tape mark on the floor near Bruce. Then, when Harriet walks in another white tape mark becomes visible on the floor by her feet. (00:03:35)
Batman Stands Pat (2) - S1-E14
Visible crew/equipment: When the Dynamic Duo trace Turkey's bowler to Mad Hatter's lair, they proceed to climb the wall. Then Hatter tells his goons to get into place for the trap, and in the next overhead shot there's a white chalk T-mark on the floor near Mad Hatter, at the right side of the screen. (00:17:45)
When the Rat's Away the Mice Will Play (2) - S1-E12
Visible crew/equipment: While Robin is "fiddling with the atomic pile" up on the scaffolding in the Batcave, Commissioner Gordon calls Batman to ask if he'd been to Gordon's office earlier, and in the overhead shot of Gordon's office there are two white tape marks visible under the desk, with one at Gordon's feet. (00:17:45)
Fine Finny Fiends (1) - S1-E33
Visible crew/equipment: When Batman and Robin enter Penguin's hideout at the South Pier, with Penguin and his goons ready and waiting for them, the duo walk to the table and both of their chalk marks (a bit smudged) are visible on the floor where each stands. Then, when Penguin captures Robin and places him against the wall, another two chalk marks are visible on the floor for each actor. (00:20:40 - 00:22:05)
The Bookworm Turns (1) - S1-E29
Visible crew/equipment: When Printer's Devil contacts Bookworm headquarters, just as he messages "plot A washout" Bookworm walks over to the desk, and the white tape mark is visible on the rug where Lydia will stand. (00:07:25)
The Purr-Fect Crime (1) - S1-E19
Visible crew/equipment: When Commissioner Gordon uses the Bat Phone and Alfred answers, it then cuts to Bruce and Dick playing crazy chess, and as the camera moves for its dolly shot, two of the crew's wood planks with marks become visible on the floor. (00:02:15)
Batman Stands Pat (2) - S1-E14
Visible crew/equipment: Batman and Robin have been captured so they're led to Mad Hatter's hat factory. When Lisa arrives, a chalk mark can be seen where she stands, and a white tape mark on the floor for Mad Hatter. (00:19:30)
When the Rat's Away the Mice Will Play (2) - S1-E12
Visible crew/equipment: While Bruce Wayne is in Commissioner Gordon's office, when the Batman imposter shows up, numerous white tape marks are visible on the rug, where the actors will step as the scene progresses. (00:14:20)
A Riddle a Day Keeps the Riddler Away (1) - S1-E11
Visible crew/equipment: After the opening credits, during the scene in Commissioner Gordon's office Gordon tells Chief O'Hara to assign an extra squad, and numerous white tape marks are visible on the rug as the actors walk around. (00:06:15)
A Riddle a Day Keeps the Riddler Away (1) - S1-E11
Visible crew/equipment: After Batman tells Robin to look up the address for the Royal Mushroom Club, when it cuts to Riddler's hideout a chalk T-mark can be seen on the floor near the wall opening, where Mousey will stand in a moment. (00:12:15)
A Death Worse Than Fate (2) - S1-E10
Visible crew/equipment: After the opening credits, in Commissioner Gordon's office, a white tape mark is visible on the floor near the corner of Gordon's desk, where Chief O'Hara is sitting, then Gordon walks over to his mark. (00:02:55)
Visible crew/equipment: After Joker reveals to his cohorts that his plan involves champagne, when it cuts to Commissioner Gordon standing with Batman at the microphone, as the camera zooms out the chalk T-mark is visible on the floor in front of Batman and another actor's mark in front of Chief O'Hara. (00:18:15)
Visible crew/equipment: When both Batman and Robin realise that even though the museum can't be broken into, it doesn't mean someone couldn't break "out" of the museum, as they rush to the museum's front doors we can see a chalk T-mark on the ground in front of the doors. (00:13:25)
Visible crew/equipment: At the end, Joker announces the unmasking of Batman and Robin, then when Joker turns and walks toward them, multiple chalk T-marks are visible on the floor where the dynamic duo are being held. (00:23:55)
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)
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