One year at my school, we took a Discover New York Trip. All of the students had to choose one location that they could visit. A few sites and links are listed below,with a link to information about visiting each site.
New York Aquarium and Coney Island: This half indoor, half outdoor aquarium shows both the wildlife in the water surrounding New York harbor and the oceans around the world.
Tenement Museum: This is an interesting museum for high school students, and is very telling of how New York was for immigrants who first moved to the Americas with nothing.
Ellis Island: Click on the picture to take you to Ellis Island's Website. Great features, great museum! 
Museum of Television and Radio This museum is great for kids, as it focuses on interests of kids: movies and tv! Great exhibits showing how things work could spark an idea in a child's mind of what they are capable of in the future!
Natural History: Check out this website for current exhibits, lesson plans, etc.
Central Park: At all times of the year, there are different areas you can visit to get an idea of the neighborhood.
Brooklyn Bridge: beautiful view of new york. Take the subway to Brooklyn, grab some icecream below the bridge, and work off the calories by walking across the beautiful landmark.
New York Public Library: excellent exhibitions, great books, and easy location on 40th and 5th Ave..
Battery Park: A beautiful view of the bottom of Manhattan, and an easy trip to Lady Liberty.
Guggenheim: THe Guggeheheim's architecture alone, designed by Frank Lloyd Wright, draws people to the building. 
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