You should look into Rockaway Beach Queens. Up and coming area, really trending right now, recently named one of the hottest places to be or some shit. It's where I run the bar.
In the next 2-3 years this place is going to explode into the next Williamsburg or something, and it's beautiful, right on the beach, in the summer I would not want to be anywhere else. You could still find 2BR places here between 1100-1500. Train goes right into the city, would probably be about a 45 minutes commute to NYU.