It depends how much you want to spend. I've just booked the Barbizon on Lexington Avenue - they have a special American Express cardholder rate - $240 for a suite per night! Their normal rate for a room is $180, but they're booked out next week for that.
If you want to stay in Manhattan, then try the Hilton on 6th Avenue, the Sheraton Centre on Broadway and the Hyatt Regency on 42nd Street.
There are some cheaper places on the West Side - I think there are a couple of Best Westerns, and they have a universal US booking number, but I don't know what it is. If money is no object, then the Carlisle on Madison Avenue is fantastic (and expensive) and the Pierre on the corner of 5th and Central park is in the best location imaginable.
Remember, the best, best rooms are always going to cost more. If you don't ask for a best one, you'll probably be looking at a brick wall. But then, New York's not the place to stay in your hotel room.