The Morgan library and museum is smaller, fabulous, and currently has a great exhibit of the original Babar artwork.
The Museum of the City of New York is also a bit more off the beaten track, and presently has a wonderful exhibit about the artistic connections between NYC and Paris, and is not to be missed if you are any sort of a fan of design and fashion.
Hmm… Interesting. Sadly, not much opened for Thanksgiving day itself (except ESB). 
Actually, I mentioned the New York Historical Society museum. The Museum of the City of New York is a completely different museum, on the other side of Central Park.delphica linked to it. Both are worth visiting.
You want NYC Museums? Hold onto your hat:
Up near where I live is the Cloisters Museum. It is a medieval art museum housed in original and restored buildings salvaged from Europe. It is better to visit in the warmer months to take in the Heather Garden in Fort Tryon Park, but it is wonderful to go in the winter as well.
You live in Washington Heights, Maeglin? 
I went to Cloisters during my last visit on summer of 2007. I think I’ll pass this time, I love the greenery and I doubt that it will be there.
I live a little north of Washington Heights, up in Inwood. It’s about a 30 minute walk from my apartment to the Cloisters.
There are wonderful concerts there as well, but none on Thanksgiving weekend.