The American Museum of Natural History - the name says it al. A museum but also a scientific research institute where mammals from all over the world and remains of dinosaurs and predators of mankind are housed. And sometimes the setting for a movie; many scenes for movies have been shot here. Of which "Night at the museum" with Ben Stiller in it is my favorite and I can really recommend that you see that before you go to this museum.
The museum can be found at Central Park West/79th street. It is opened daily from 10 until 5:45, except on Thanksgiving (the 4th Thursday in November) and December 25th. You can order your tickets here.
Across from the American Museum of Natural History is the Shake Shack. Super popular, great milkshakes and burgers. Just in case you're hungry ...