AMNH is a great museum for families. It has exhibits about the natural world. The dinsosaur exhibits are amazing, so are the earthe and space science exhibits. Their yearly Butterfly Conservancy is one of the most fun places to go in all of NYC. The AMNH also shows documentaries. It's a huge place, too big to really do well in one day, so plan ahead of time.
This is a timed entry exhibit and it costs extra, so get the tickets when you enter the museum. This is a room full of live butterflies. The butterflies are every color imaginable, and they're flying all around the room. Sometimes they land on you. I've had them land on my hand or arm, which was cool, and once on my face, which was less so. Butterflies don't sting or bite, so it didn't hurt. It was just strange. Many, if not most, of these species are tropical, so the room is warm and humid, about 80-85 degrees Farhenheit, so expect to sweat. Absolutely one of my favorite places.