You can't go up the Statie of Liberty, but you do breeze by it on the ferry to Ellis Island, so that might be a good option. Then again, you don't have any museums on your list (MOMA, Guggenheim, the Museum of Natural History, etc.), and Ellis Island is essentially just a museum, so maybe that's not your cup of tea.
Lots of people say you should catch a Broadway show while you're there, but if you haven't planned that out already, it's probably way too late to get tickets.
I went to New York a few years back and my favorite memories were just walking around. We walked up Broadway from 26th (I think) through Times Square, up to Central Park, through the park all the way to Harlem, then took the subway back. It's a fantastic city for walking around in, especially on a street like Broadway where you'll recognize landmarks every 10 feet. Central Park is absolutely amazing, had a blast just sitting there people watching.