Between Thanksgiving to just after New Years is one of the busiest times for hotels in New York, so don't expect any deals. Occupancy is very high, mostly tourists from out of the country, and since they don't usually look for bargains, the rates are very high, and rooms are few and far between.
You could also look into Jersey City, New Jersey. A short train ride under the river and rates should be about 1/3 lower than they are in the city. Or even lower.
If you were going to try priceline I would say make a reservation someplace you can cancel just in case you can't get a room through Priceline.
Honestly, anything for under $300 in New York at that time is probably a good deal.