Of the ones they list, there were a lot about gay culture, or the unpleasant side of New York that makes me not want to live there. Such as Dog Day Afternoon, or Fort Apache the Bronx, and Taxi Driver.

Of the ones listed that I enjoyed and portrayed New York in an appealing way, I'd list Three Days of the Condor, King Kong (1933 version, but I enjoy all three), and the Christopher Reeve Superman movies. Some I don't even think of as New York movies like The Godfather, The Muppets Take Manhattan, American Psycho, Breakfast at Tiffany's, West Side Story, On the Waterfront, Saturday Night Fever, The French Connection, Escape From New York(despite the title, it doesn't look at all like New York), Rosemary's Baby, and Goodfellas.

The Warriors (1979) falls in the ugly subculture category, but it was delightfully silly and unintentionally funny, and it did show a lot of parts of the city, and on some levels I thought captured well New York in the 1970's.
Still of the Night(not even listed!) with Roy Scheider and Meryl Streep (1983) similarly captured New York in the 1980's.
Wall Street (1987) also.
And the Woody Allen movies, although a whiny neurotic mostly Jewish side of New York.
And the two Ghostbusters movies!

Their number one pick is Taxi Driver. That would not be my number 1 pick. My favorite New York movie is It Could Happen To You with Nicholas Cage and Bridgette Fonda, which again, isn't even listed.

I've often thought of New York City as the most photographed and romanticized city in Hollywood films, and perhaps in the entire world. Oddly even more so than more Hollywood-local Los Angeles.