I haven't found a definitive list of power racks / safety squat racks in NYC gyms, and they are rather hard to find. My ideal is to have power racks that you can squat, bench, and press in. I'll put what I know so far. There's some additional commentary here that I haven't verified.
Mid-City 49th St
2 safety squat racks. Not set up to bench in, but I suppose you could drag a bench over from somewhere. I haven't attempted to do so. Fine to press in.
1 safety squat rack, 1 power cage. Not set up to bench in. Don't recall how pressing would go - I was in on a 3 day pass.
A Starting Strength friendly gym. See the overview here. In the Complete Body and Spa on 18th between 5th and 6th.