Metroplitan Museum of Art is a must
Museum of Natural History/Planetarium are also a must
Go see the architecture of the Guggenheim
Walk along 5th Avenue from 57th street to 34th Street then go to 6th Avenue to Empire State Building.
Barnes and Nobles on 17th and Union Square North is a must if you love books.
Central Park is rather drab now but still pleasant.
Walk around West Village, its fun.
See the United Nations if thats your thing. There is more of course but ummm try and take a tour on one of the double decker busses. They arent bad.