If it’s your first trip I’d say take the Staten Island Ferry.Not because Staten Island is a must see...but because it passes right by the Statue of Liberty and the view is breathtaking.Also,you’ve gotta do the Empire State Building but expect a long line on a summer weekend..
The Circle line Cruise around Nanahattan is fun.
http://www.circleline42.com/new-york-cruises.aspx?gclid=CLyq177hoKICFQuB5QodEjPDzA
Contrary to what some have suggested, I would skip the Circle Line. Parts of it are boring, it takes a big chunk out of your short visit, and it isn’t really seeing New York.
Sunday, June 27, is the gay pride parade. You may want to go and be outraged, go and enjoy it, or avoid Fifth Avenue while it is going on if you have to get anywhere.
Dusk is the best time to see Times Square. Or if you get there slightly before theater time, you will see NYC energy at its craziest. Also Grand Central at rush hour: stand on one of the staircases and watch, and then attempt to walk through it.
I would skip the Cloisters also. It’s a long trip up there from where you’re staying and it’s more suited to a long day with lots of time.
Other thoughts: The Harlem tour bus if you want to take one of those tours. The Madison Avenue shops from the fifties up through the seventies. You’re going to be staying near the SoHo shops too—good shopping and celebrity watching.
Have a wonderful time in New York, where every day is Christmas and every night is New Year’s Eve.