Manhattan is enormous and you’ll find an infinity of things to skate around the LES Skatepark and around the nearby City Hall. You’ll also find many good spots around the streets of Midtown and many plazas around the financial district, although be cautious as you know that skateboarding this city’s streets isn’t welcome with the authorities.
From a tourist aspect, if you look around, the buildings are enormous and the City Hall is admirable. You could go to see the Brooklyn Bridge, the New Museum, the World Trade Center, Battery Park, Soho, the 11th September National Museum and Chinatown as they are all interesting places. Other places to see in New York are Central Park, Times Square, Williamsburg Bridge, Bedford Street, Flushing Meadows-Corona Park, St. Marks Street, Union Square, the Statue of Liberty and much more!