If you want a quick well-rounded tour, you can take one of the bus tours. This will point out all of the major tourist spots in about 90 minutes or 2 hours.
Specifically, I think Little Italy, Central Park, Time Square, heading to the observation deck at the top of the Empire State Building, stepping foot into the massive Grand Central Terminal, and the Metropolitan Museum of Fine Arts (the MET) are some of the must-sees. There are also plenty of comedy clubs, bars, and clubs to take advantage of during the night hours.
If you're feeling adventurous, you can take a cab or walk to the South Street Seaport and cross the Brooklyn Bridge by foot.