North New York is an archaic name for an area of what is today the Mott Haven section of the Bronx. It was between 134th and 147th Streets and from Port Morris to Third Avenue.
Example Usage of Bronx,
fortheinsane: @reneeruin well you have to be cool....I met you through The Bronx and @jormahchrist....does it get any cooler?
NewYorkCP: New York: Bronx homes glitzed with elegant and over-the-top lights http://bit.ly/7S2MuW
Purupuru: Curse you, Bronx sidewalk of icy death!! Missed the express bus because I couldn't get down block faster than a turtle D: