We took a short trip with friends last February. I have been to NYC many times (live close enough to drive in for the day), but they had never been. We did the NY Water Taxi one day. It was great. You hop on and off. They take you down to where the 9/11 Memorial is, and you can even get a water taxi package that includes the tickets for the memorial (they are free, but it just kills two birds with one stone). It sails past the Statue of Liberty too, so you can take some nice photos.
The other thing we did was a free tour of the NY Public Library. It's an hour in length, and they give you the history and show you different points of interest in the library. Google it for times. I've done it three times now with three different sets of people- it's good stuff! And did I mention FREE?!
Central Park is AWESOME and you could seriously spend all day there and still not see everything. But fun to poke around, and good people watching.
If you can catch a show, Wicked is fantastic. But you can also wait in line at the TKTS booth in Times Square and see what you can get day of for "cheap" (beware, nothing is really cheap- but the tickets are discounted).
I've been on the top of both the Empire State Building and The Top of the Rock. Both have spectacular views. The Top of the Rock is closer to Times Square so if time is an issue for you, it is just as good
So much to do in NYC and so little time! Have fun!!!