Of course the Statue of Liberty is a must see, but it is currently closed due to damage from Hurricane Sandy. There are a few ways to get a look. You can take the subway to Battery Park and see the Statue off in the distance. My grandchildren were thrilled to see the lady, even from this distance. The park also suffered hurricane damage, so it's not a place to relax on the lawn right now. This route combines easily with a visit to the wonderful Museum of the American Indian, a branch of the Smithsonian. You would walk right by it en route from the subway.
Another strategy would have been to visit Ellis Island, but it is currently closed, too.
Still another option would be to enjoy the closer vantage point from Liberty State Park in NJ, but you should check with the park to see if the viewing area is open as this park also suffered storm damage.
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC.