I loved going to the Empire State Building when I was 8, myself. I also enjoyed walking around and taking it all in.
Central Park Zoo and Statue of Liberty is undoable in a day, I can tell you that right off the bat. Complete opposite ends of the city!
I'm assuming you're not seeing a show, or I'd suggest The Lion King or Mary Poppins. Sadly, there's not much for an 8 year old to see on Broadway these days, what with the closings of Shrek the Musical, Beauty and the Beast, Tarzan, and The Little Mermaid.
Definately walk around and perhaps see the more historic sites in the city? The Natural History Museum might interest her as well.