Museum of Natural History. In my opinion, its one of those places that makes our city a trillion times better than any other. It amuses me this is a "science" museum:
Make it a full winter experience and combine your visit with a Planet Earth marathon beforehand. This way you can impress your friends with esoteric facts about the animals on view. Naming the dietary restrictions of the Alaskan Brown Bear will make you surprisingly popular.
Bring patience and a good attitude - there are a lot of strollers and children. They wont ruin your time there, but they will certainly up the intensity. I actually left feeling like a huge five-year-old. Its hard not to when you walk through halls filled with dream-world dioramas containing literally millions of some of the craziest species you've ever seen. You will revisit those feelings of wanting to be an archaeologist when you grow up.
Take the B or the C to the Upper West Side and plan your trip for New Years Eve day. I cant think of a better way to end the year on a good note.