Only one person mentioned Avenue Q!!! That show is amazing and hysterical and you really should see it. It's great. I haven't seen a whole lot of Broadway, but I have seen a lot of theatre and that's on my top five list.
See it! Rush tickets are $21.25 (I think), and they're the front row - so the actors and puppets are RIGHT there, it's an amazing way to see the show! Wicked is supposed to be amazing too, cool people in that, but I don't know. I would skip anything that's been there for years - that's me being a theatre snob, but hey.
I think ice skating in Rockefeller is over-rated, I like the rink in Central Park more - it's pretty at night. I like Strawberry Fields in Central Park too.
The Met is amazing... you could spend days in there.
Me being a dork - there is a new American Girl store (they make historical fiction dolls - I had one while growing up and she is a prized posession and basically my favorite toy ever, so this was very cool to me) that is like three stories and huge and has everything. I really enjoyed a visit (and talked some woman into buying her daughter a Molly doll - I should get commission!) so I don't know, you might want to check that out.
Oooh, the Soup Nazi! Very pricey but very good soup. Best soup I've ever had. And he's just like on Seinfeld... it was scary. I had to psych myself up to order. He's on... hm. 55th and Broadway? I'm not sure, it's somewhere around there.