When I was younger and broke(r) I always stayed at the West Side Y, off Central Park West and a stone's throw from Lincoln Center.
For around $100 a night you get a private room, semi-private bath, very rude (although helpful) staff, and a great location to most of what you would want to do in Manhattan.
If you don't mind spartan accommodations and aren't planning on spending that much time in your room, one of the YMCAs of NYC is a great deal.
"...ah, gays and their wit. Hell must be a laugh a minute!"
-Evie Harris