Christmas is a great time in NYC. I spent Dec 25 there once on the streets as my hotel's heating had packed up and it was minus 20something outside. Fortunately cinemas, theatres and churches were open, and some shops. Stroll down 5th Av just admiring the Christmas windows, as well as doing the things others have suggested. But do be prepared to wrap up warm, just in case.
You can also skate, or watch the skaters, in the Rockefeller centre. I had Xmas dinner in the restaurant inside while I watched.
And everything is now supercheap.