I have been here twice - once with my family, and once by myself.  I recommend arriving right when the museum opens, because the lines get long and the museum gets crowded really quickly, especially on school days or during the summer when day camps come to the museum.
The museum is HUGE (four floors), so if you only have a day to visit, take a look at their web site www.amnh.org to see a list of some highlights and plan your visit.  Or, you could do what I did: find as many exhibits as possible that were in the movie "Night at the Museum."  It took me about three hours and took me through all four floors - really fun!

AMAZING place, just the most interesting museum (for me), the most realistic, etc and you MUST see : Journey to the Stars. It is an engrossing, immersive theater experience created by the Museum’s astrophysicists, scientific visualization, and media production experts with the cooperation of the National Aeronautics and Space Administration (NASA) and more than 40 leading scientists from the United States and abroad.

I love this museum.  It reminds me of my childhood and still has those cool diorama displays many places are lacking these days. Really informative and a heck of a lot of fun to spend time in (if you are a science geek like me)!

I love the top floor with all the recreations of dinosaur fossils. I was a huge dino fan as a kid and still am. This place evokes the child in you!

Huge. Go with people that you don't have to stick with so you can take your time looking at what you want to.