There is no city like Gotham City. Okay, yes, that's a bit on the nose, with Gotham being fictional and all. And it's hard to say that any other city, both real or imaginary, could be anything like the one which claims the Batman as a citizen. But Caped Crusader (and assorted allies and enemies) notwithstanding, there is no city like Gotham because Gotham in an amalgam of so many different places.
Most people assume that Gotham is meant to be a fictional version of New York, yet Christopher Nolan filmed the two most recent Batman movies in Chicago and no one seemed to notice. This is because Gotham is meant to be any big city in America, any place with back alleys, abandoned buildings, and a skid row. Aside from the fact that it snows in Gotham, it could just as easily be downtown Los Angeles as anywhere east of the Mississippi. That's part of the appeal and the genius of Gotham; at its core, it's relatable. You don't have to live in New York to know Gotham City; you just have to read an issue of any of the numerous comics featuring the city.
But Gotham also transcends the definition of a city. It's not just a setting, but a story in and of itself. It changes into whatever it needs to be, depending upon the story being told. Superheroes fighting in the sky above? Gotham's the place for it. Petty criminals struggling to surive and organized crime strangling the life out of the city? It's going on right now. High tech, intelligence brokers helping good guys and bad? Accessing your bank account as you read this. And let's not look past that quaint little insane asylum that seems to have a revolving door for an entrance. Flying saucers, flying cars, flying men, flying bullets -- it's all just a matter of which block you're on, or which comic you're reading.
You never now what you're going to get with Gotham City, which is unique among both real cities and fictional ones. Unlike most imaginary cities, Gotham is a part of a serial story that has been going on for 70 years and shows no signs of coming to an end. Gotham has changed from decade to decade and will continue to do so as long as there's a man dressing up like a bat and fighting crime. No other city can claim the things that Gotham can, and no other city has such an unknown and infinite future.
For those interested, I would recommend three books to see what Gotham has and can be. Batman: The Black Casebook features the brightly colored Gotham of the 50's and 60's, when Batman faced foes from other worlds and other dimensions. Batman: The Long Halloween tours both the world of organized crime in Gotham and the breed of costumed criminals that Batman contends with throughout a single year. Finally, Gotham Central is the story of the Gotham City Police Department, those men and women who have to solve both ordinary and extraordinary crimes while under the shadow of the Batman.
Gotham City: where anything can happen...and usually does.