New York's subway stations are stilled marked on the street by a big "M", and you'll occasionally hear people say "metro," but "subway" is much more common -- it is the Metropolitan Transportation Authority, though.
In Chicago, which has another pretty old mass transit system, people call it the "el," even the parts that aren't elevated (i.e., the subway, though you'll hear "subway," too). Oddly, the commuter rail between Chicago and suburbs is the "Metra".
Does the New York Subway have a logo? I know the MTA does (it's kinda cool) but most New York subway street signs just have little roundels indicating the various lines through the station.
It's never called the Metro here. The Metro is a free newspaper.