Awww I'm so jealous, it's a fantastic place!
Definitely go to the top of the rockerfeller center at night when everything's lit up, costs about $20 but is sooo worth it (we did ESB by day and there at night).
Little Italy's Mulberry St is great for lunch.
The bus tours are good to get about, we walked most of it then did all three tours in one day (uptown, downtown and Brooklyn and Night). You get so much info if you get good guides, a proper NY'ers guide. They tell you where the stars live and all kind of stories.
The night tour is great as they take you to the Hulton Ferry landing to see the Manhatten skyline at night (from Brooklyn).
The Brooklyn tour also gives you chance to get off in Brooklyn and walk back over the Brooklyn Bridge.
As you can't go up the Statue of Liberty, we just took the free Staten Island Ferry there and back as you get a great view.
The funky show off of a polar bear in the little zoo in Central Park is good and if you were a Beatles fan or John Lennon fan, Strawberry Fields, the shrine to him in Central park is very thought provoking.
We found this great diner for breakfasts...
http://www.menupages.com/restaurantdetails.asp ?neighborhoodid=0&restaurantid=3617
Service is quick and brusque but great food (and lots of it!!!).