"Batman" comic books have changed so much since the 1966 TV series was on the air. Darker, more violent, and always adding in details that were never even dreamed of for the show. For instance, the revelation of the Riddler's name as Edward Nigma. (Of course nowadays they seem to be peddling back from that one. I mean, really - E. Nigma? The splainin now is that it was a very contrived alias.)
But the Toobworld Dynamic doesn't have to adhere to those enhancements that came after the fact. Currently, 'Gotham' has just begun its depiction of the Joker's origins - whether it's in line with what is considered canon in the comic books, I don't know. But I do know that the identity of the Joker and how he came to look like that never came up in the original TV show, so I'm not beholden to use it. For the benefit of the Toobworld Dynamic, the Joker was actually Victor Gervais, AKA Krispin Kinsey, which links 'Batman' to both 'The Man From U.N.C.L.E.' and 'Get Smart' thanks to the three roles being played by Cesar Romero.
The Penguin's true identity was never revealed either, and for years I have resisted "Oswald Cobblepot" as the stupidest name ever coined for a character. That is, until 'Gotham' suggested that Cobblepot is an Americanized version of his mid-European family name of Kapelputz. I can live with that. However, I think Burgess Meredith's Penguin would have changed it in order to have a sound as "sophisticated" as his attire, so that one of his aliases from the 1966 movie (absorbed into the TV Universe) - P. N. Gwynn became his legal name.
As for the previously mentioned Riddler? Frank Gorshin was playing murderer Lou Rydell who must have escaped from an insane asylum (from an episode of 'The Alfred Hitchcock Hour'.) Somebody in the asylum must have mispronounced his name of Rydell as Riddler and it stuck. And when John Astin briefly assumed the nom de crime... well, he was actually Gomez Addams! (And you should know where he comes from!)
This all brings me around to the location of Gotham City and where it can be found in the continental United States of Toobworld.....
I've seen several references to Gotham City being found in New Jersey, most prominent of which would be the Atlas of DC Comics from the 1990s. (And Metropolis would be close by, located in Delaware.) But that wouldn't work for the main Toobworld and it's the TV show itself which negates that idea, not just some preferred theory of my own.
In the Bookworm story, this van showed up on the bridge leading into Gotham City:
Forget about the Chrysler Building showing up there in the background - it's a common practice in Toobworld for architecture to be repeated elsewhere. The important point is painted there on the side of the van - the call letters for that TV station.
Any TV station that began with the letter "K" would be found west of the Mississippi River. Eastwards, they all begin with "W". And so this couldn't be New Jersey, it has to be somewhere in the Western United States.
Next we have to look at a few key scenes from the 1966 movie, which as I've stated before, has been absorbed into the TV Universe. At one point, Batman had trouble trying to get rid of a bomb on the waterfront. I suppose arguments could be mounted that Gotham was situated on the shores of one of the mighty rivers transecting America, or perhaps one of the Great Lakes.
But then the Caped Crusader is attacked by a shark!
So it has to be ocean front property on the West Coast. Gotham City must be located in California.
And as far as Earth Prime-Time is concerned, so it shall always be....