The nice thing about doing the Statue of Liberty is Ellis Island is almost always packaged with it - you get to see both islands for the same price.
If you love architecture like I do, there are several buildings that you must check out - Woolworth building, Flatiron building, St. Patrick's, Rockefeller Center, Trump Tower, Empire St Building, Chrysler Building, Grand Central Station. I'd also say check out Citicorp Center as it's one of the oddest buildings you will ever see (although I have yet to see it myself)
The cool thing about the Empire St Building, Chrysler Building, St Patricks, Trump Tower, and Rockefeller Center is they're all relatively close to each other - all in midtown. I'd recommend going up to the top of the Empire St Building as you get an incredible view of the city up there (I think you can also see 8 different states while up there - New Jersey, Pennsylvania, New York, Connecticut, and others).
If you get the chance, I recommend checking out Fire Island/Jones Beach on Long Island. Incredible historical beach. If you head further east on Fire Island there's a pretty sweet lighthouse there as well.