You picked a bad time.

I'm sure many families, couples, etc are planning on a nice getaway for new years. You will probably have a lot of trouble finding something if you didn't book it a while back.

Do you have a chain preference? I know the Hilton Garden Inn, at LIR has some openings for $124/night per room. I'm not sure how reasonable that is to you, but for a New years booking on short notice that's probably not too bad.

Kayak pulled up the Best Western at $59/night per room and a few others that might be best avoided.