The Statue of Liberty, the Highline Park, Hudson River Park, Chelsea Market, the World Trade Center, Grand Central Station, the Metropolitan Museum, MOMA, the Museum of Natural History... You could also do something more original- there are a lot of smaller museums like the City Museum of NY (I think that's the name), the Tenement Museum, the Guggenheim, the Frick, the Cloisters, the Whitney, the Brooklyn Museum of Art, the Museum of the the Moving Image. I hope you like museums! Actually, I prefer art galleries to museums- there are entire neighborhoods filled with art galleries that are free to visit, Chelsea and the Lower East Side. You could also do a walking tour. Some interesting neighborhoods might be the West Village or some Brooklyn neighborhoods (check www.yelp.com). There is plenty of theater to be seen in NYC. Sometimes it can be pricey though. There are so many live entertainment options for every budget, but you have to do some research. I personally like to see dance at the Joyce theater and the free performances at Lincoln Center's David Rubenstein Atrium. Try www.theskint.com or www.villagevoice.com for starters.