How about Serpico 1974, After Hours 1986, the Wanderers 1979, Night of the Juggler 1980 to name of a few?

Die Hard: With a Vengeance is also a very New York movie, except the last few minutes, when the setting moves to Canada.

Beat Street (1984)
Hangin' with the Homeboys (1991)
Juice (1992)
Krush Groove (1985)
_
Every person that served can be called a veteran, but not every veteran can be called a Marine.

Death Wish?

The French Connection with Gene Hackman and Roy Scheider, despite his title it's along with the Warriors the most New York movie in my opinion. It's practically a sighteeing of New York in the 70's. Legendary movie.

"The Warriors" is one of the best New York subway movies without being actually about the subway (like Taking of Pelham 123) and a great New York movie generally.
There are a lot of great New York movies from the 1970s. Taxi Driver, Cruising, Panic in Needle Park, Annie Hall, Manhattan, Mean Streets, Saturday Night Fever a few that come to the top of my mind.

The Taking of Pelham One Two Three
http://jmoneyyourhoney.filmaf.com/owned

At least they killed someone !

The gangs in West Side Story didn't seem very threatening.
"Grease" took place in California, but had a lot of New Yorkers in the cast.

I'd also say that
Klute
and
West Side Story
are also very New York movies, as well. Both of these films reveal the seamier side of New York City, but that's what makes both of these films as interesting as they are.

That is a good point. Woody Allen movies are very New York, but that is the bourgeoisie New York. "The Warriors" was the poor, decay-era New York. Woody Allen's characters take taxis and limousines. Characters in "The Warriors" traveled by subway or by foot. I think Woody Allen used actors who were based in New York, but not necessarily New Yorkers. I think there were a high percentage of actors in "The Warriors" who were born and/or raised in New York. Some of them include Dorsey Wright, Brian Tyler, David Harris and Mercedes Ruehl.

There are many others. Taxi Driver is another. Mean Streets as well. Heck, just take most of Woody Allens films from the 1970s and 1980s.