I don't think there's much instruction or 135 to be had in the city itself. There might be some positions available out of ISP, SWF, HPN or TEB, and it would be a little cheaper to live in the outskirts anyway.
Many of the airline types who are based out of LGA or JFK live in the Kew Gardens/ Forest Hills area, and some of the freight dogs live out towards Long Beach.
Try to find a gig first, and then look for accomodations. It would be nice to be able to take public transportation to the airport, since having a car in the NYC area is extremely expensive, and traffic is horrendous 24/7.
Good luck!