Ellis Island and the Statue of Liberty are a must see. Get to the Liberty Island Ferry early to catch the first boat. Plan on spending 2-3 hours.
When you get back from Liberty Island, you’re within walking distance to Wall Street, Ground Zero and St. Paul’s Chapel, the New York Stock Exchange, Fraunces Tavern (where George Washington bid farewell to his men), Federal Hall (where George Washington took his first oath as president) and the South Street Seaport.
The American Museum of Natural History is fabulous. There are lots of dinosaurs, medieval art, and the Hayden Planetarium.
DO NOT TAKE the double-decker buses. They are not safe. You will be safer taking your own tour.