Coney Island, Brooklyn
The Stillwell Avenue Station has been totally re-done. It's quite a sight.
Also, try to catch a Cyclones game, if you can! It's a great stadium, and it's not as expensive as Yankee Stadium!
If you take the F train, D train, or Q train to West 8th Street in Brooklyn (all the way down!), you will be able to experience Coney Island. Beginning at 11AM until 12 midnight (May through September - other months, on weekends and holidays only) , the stores open, the stands begin cooking food, the rides start spinning, and the boardwalk fills up. There is a beach (cleaner than ever), Nathan's Famous hot dogs, fries, and other very healthy food, an amusement park, loads of people watching, and of course, the freak show. All the people watching is free. The rides charge individually. The beach is free.
Right by all this fun is the New York Aquarium! It's open 10AM through 5PM every day. It's pricey at $12 for adults, and $7 for seniors and children. Most people like it, however.