Once Upon a Time in the City of New York

Only the Pilot was filmed in New York.

Then, when the show was produced, all the filming was done in Los Angeles.
For this reason, many things, especially Catherine's apartment and balcony, are different in this first episode.

This famous scene, included in the opening credit, was filmed in front of the Dakota Apartments, Central Park West, NYC:

This is the same corner, from Google Map Street View.

This is the view of The Grate, on the other side of the road.