Torker makes a few models in your price range:
http://www.torkerusa.com/

A single-speed freewheel bike is a nice and simple and will be fine for 99% of NYC terrain, if you're not hauling too much stuff. An IG bike like the Torker Graduate has most of simplicity of a single speed, plus the advantage of gears.

You can go fixed, too, but if you are a self-described newbie I would concentrate on getting comfortable riding in the city and not worrying about getting used to riding fixed at the same time.