*The Adam West "Batman" TV series - A pop art version of Boston since one episode references a "Gotham Rock."
*The Tim Burton films - An Art Deco and Art Nouveau (or perhaps more specificially, Expressionist architecture as seen more often in "Batman Returns") flavored version of Vancouver, British Columbia, Canada. I'm only saying Vancouver since in the first Burton Batman film, there's a map of Gotham that is actually, an inverted map of Vancouver. It's been a while since I've seen "Batman '89" and "Batman Returns" in one showing, but since Anton Furst did the production design for "Batman '89" and Bo Welch did the production design for "Batman Returns", Gotham must of had somewhat of a different flavor/style.
*"Batman: The Animated Series" also appears to be heavily influcence by the Art Deco look. I would guess that "Batman: The Animated Series" could be an Art Deco version of Long Island, New York (more specifically, Queens).
*The Joel Schumacher films - Manhattan crossed with Neo-Toyko (a la as seen in "Akira" or any other subjects relating to the cyberpunk culture/genre).
*"Batman Beyond" - Futuristic architecture that mixes Gothic and Asian influences. Since "Batman Beyond" is canonical with "Batman: The Animated Series", I'm going to suggest that it's a futuristic version of Long Island.
*"Batman Begins" - A souped up version of Chicago.
It's probably more difficult to narrow down a specific look for the comics since various artists will depict their own versions of Gotham. Although for the most part, Gotham was been implied as an exaggerated version of New York City. The locations have either mostly been implied to be in the place of Manhatten or Vancouver.
*Post "No Man's Land" storyline - Modern architecture (with glass skyscrapers and buildings).