It's generally considered that there are two periods in New York film industry, the pre-Giuliani and the Post-Giuliani one.
The pre-Giuliani, spanning from the mid-60's to late 80's, was characterized by an grim and gritty style mostly composed of anti-heroes, a lot of them detective, using violence to get their way. Most of the memorable (if not all) films are set exclusively in New York City. Since a lot of those movies didn't have any major backing a certain crudeness can be perceived from those movies which sold relatively well outside of New York. With time a style of intellectualism started to develop.
An interesting sub-genre can be found, the black movie. Mostly made through the 70's, most of those movies were for subject the search for identity and a lot of can be found among the Finest New York gave. One of the most famous being Fight Club, about a young underground boxer name John Shaft who struggled to clean up his life after a life of crime.
In the Post-Giuliani, most of the action was situated out of New York (Mostly because of New England's occupation of the city), idolizing the life outside, and producing movies with nationalistic and often moral overtones. One the era's most known movies was Braveheart, telling of Giuliani's participation in the battles of the civil war, but in real life he was born later.