A few months back I went to the Museum of Natural History for the first time. The museum is one of the most famous NYC museums full of fossils, a planetarium, ocean life, bones, and a gigantic (fake) blue whale. It was really cool to see all of the dinosaur fossils and walk around the exhibits, but the AMNH is a really old-fashioned museum. It feels like some of the exhibits haven't been updated since the 1950s... and as a huge Mad Men fan, that's okay too. :) I will say that I think Chicago's Natural History Museum is a bit better. :)
I definitely recommend lying on the ground and looking up at the big blue whale. Kind of feels like you're in the ocean.