NYC is actually VERY film-friendly, even if you're an indie filmmaker with nothing but pocket lint. First, stating the obvious. If you're not using more than a tripod and otherwise hand-held equipment, you can film wherever you want in NYC as long as you let people through when they want to go through.
Before he became known as America's most famous artist in the 1930s, Thomas Hart Benton was painting backdrops for filmmakers in Fort Lee, New Jersey, known now as the first Hollywood. That's right: Between 1913 and 1917 Benton was watching and assisting film directors as they told their stories on a huge scale. And he took copious notes.