Like Tintin's age, Wolverine's daily lager intake, and the number of birthmarks on Popeye's body, the exact location of Gotham City is one of those comic book mysteries we will likely never receive a firm answer to.
We can however look to a litany of conflicting and dubiously canonical sources to get a rough idea of where Batman's stomping ground sits on planet Earth. Who knows? You could be living in Gotham City right now, completely unawares — that is until Killer Croc and Kite-Man burst through your living room wall.
Right from the start, the location of Gotham City was nebulous. As Batman co-creator Bill Finger admitted in 1970:
Originally I was going to call Gotham City "Civic City" [...] Then I tried "Capital City," then "Coast City." Then I flipped through the New York City phone book and spotted the name "Gotham Jewelers" and said, "That's it," Gotham City. We didn't call it New York because we wanted anybody in any city to identify with it."
You can see a modern version of Finger's "every-city" principle in director Christopher Nolan's Dark Knight trilogy, which incorporated chunks of Pittsburgh, Los Angeles, Chicago, New York City, and Newark, New Jersey into Gotham City limits. And since Finger coined the name, the comic book location of Gotham bends to the whims of whomever the hell's writing Batman.
And decades of writers not coordinating their Batman scripts has led to some contradictory cartography. For example, in 2003's Planetary/Batman: Night on Earth, Warren Ellis sums Gotham up as "old as New York, founded on the East Coast and originally designed by English masons on opium [...] exacerbated by absinthe-fiend local architects in the twenties, [and] basically not suitable for habitation."
But Gotham also has been hit by earthquakes (1999's No Man's Land story arc at left), sits in the Central Time Zone (Man-Bat #3), and was a cowboy town in the 1800s (2011's All-Star Western). Heck, if we interpret all of the above criteria extremely loosely, Gotham City could sit on South Padre Island, where Batman rescues co-eds year round from their own vomit.
So yes, it's a fool's errand to pinpoint Gotham in an atlas. But the true fun begins when artists go ahead and slap Gotham on real-world maps, like in this 1978 World's Greatest Heroes comic strip, which dropped Gotham over Bridgeton, New Jersey and eradicated Dover, Delaware with Metropolis.
And in the 1990 atlas to the DC Heroes roleplaying game by former DC editor Paul Kupperburg, New Jersey is deformed by the tectonic forces unknown — does the Delaware River exist in the DC Universe? — but Gotham still sits squarely in the vicinity of Vineland, NJ. Metropolis, on the other hand, has slid down over the Delaware towns of Seaford and Laurel. (Notice forlorn New York up there, "the Cinderella City," eclipsed by its two "ugly stepsisters.")
But hey, this is comics we're talking about! Next week, the dreaded Anti-Monitor could accidentally fart Herb Alpert's "Spanish Flea," which would rewrite reality and transport the state of Iowa a few miles off the coast of Papua New Guinea. Moral of the story: never buy real estate if you live in a comic book. It's a renter's market.
Semi-related: Did Batman go to Yale?