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.
Batman Stands Pat (2) - S1-E14
Visible crew/equipment: When Mad Hatter is sending Lisa in to butter up Mr. Bowinkle, the microphone shadow is bobbing up and down above their heads. (00:11:25)
Batman Stands Pat (2) - S1-E14
Visible crew/equipment: When Batman and Robin use the Batmobile's Detect-a-scope to locate Turkey's bowler, as Batman notes that Hatter's hideout must be in the old warehouse, the reflection of the boom pole/mic is visible at the right side of the Batmobile's bubble windshield. (00:16:55)
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)
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)
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)
Visible crew/equipment: At the end Harriet surprises Bruce and Dick with a rehabilitated criminal, and when Blaze walks in we can see the shadow of the moving boom mic on the left side of the screen. (00:23:05)
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)
Better Luck Next Time (2) - S1-E20
Visible crew/equipment: While Batman uses his metal claw to hang from the wall, he reverses his communicator's polarity and increases the audio modulation. It then cuts to the tiger, and at the start of this shot we can see the animal trainer's red gloved hand, at the bottom left corner of the screen. (00:04:40)
Visible crew/equipment: Outside Madame Soleil's, when Riddler notices the Batmobile he rushes up to it with Tallow following behind, and the chalk T-mark is visible on the ground at Tallow's feet. As this shot continues, when Tallow warns Riddler about the Batmobile's burglar alarms, the reflection of the boom pole/mic is visible on the glass. (00:19:10)
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)
The Pharaoh's in a Rut (2) - S1-E28
Visible crew/equipment: After Tut's henchmen carry "Bruce" from the mansion, Robin tells Alfred to meet him in the Batcave, and as Alfred walks toward the foyer a crew member is visible past the doorway, at the left. (00:11:30)
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)
While Gotham City Burns (2) - S1-E30
Visible crew/equipment: When Batman and Robin use the Batmobile's high energy radar to probe the giant cookbook, and also when they use the Bat-magnet, the reflection of the moving boom mic/pole is visible on the bubble windshield. (00:11:40)
While Gotham City Burns (2) - S1-E30
Visible crew/equipment: After Gotham City PD show up at the giant cookbook with the Dynamic Duo trapped inside, when Gordon, O'Hara, and the officers are standing at the cookbook's cover, the chalk T-mark and other chalk marks are visible on the ground. (00:15:50)
The Riddler's False Notion (2) - S1-E32
Visible crew/equipment: When Commissioner Gordon apologizes to Batman, the Caped Crusader tells Gordon to be careful from whom he accepts free lemonade, and during this conversation the reflection of the boom pole/mic is visible on the Batmobile's windshield. (00:03:40)
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)
Batman Makes the Scenes (2) - S1-E34
Visible crew/equipment: When Penguin and his fine finny finks return to South Pier with the umbrella filled haul, just as Penguin tosses money at his henchmen, we can see the chalk T-mark on the floor under the table. (00:18:15)
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