Definitly take in a show on Broadway or elsewhere. Also the Madam T...something Wax museum at Times Square was alot of fun, and so was the Toys R' Us. We originally were going to avoid 'ground zero' as we heard it was just construction but we ended up going anyway since we were in walking distance when we visited battery park, - I would recommend going, I am really glad we went.
As for transportation, it's cheapest to buy a weeklong subway pass (a little swipe card) since you will be using it very often to get around. I was also recommended a magazine called "Time Out New York" which you can buy at any of the magazine stands on the street, and it lists all shows, concerts, gallary openings, restuarant openings etc. that are going on that month, it was cheap and worth it.
If you like Natural History, well hit up the Natural History Museum, they have a life sized replica of a blue whale!
