Meatpacking district, check out quaint boutiques, shops, and Chelsea market.
New York philharmonic orchestra, everyone can recognize and appreciate great music even though they are not interested in classical music in general. Give a shot. It is worth it.
American ballet theater, get a student rush ticket.
UN headquarters, book a tour before you visit.
The cloisters, medieval art with quaint architecture.
Yankee stadium, want to try cheapish hotdog and beer with hot and humid weather?
Central park reservoir, if you are passionate about running, they have great track with awesome view.
Pier 16, lovely shops, peaceful atmosphere, and sometimes awesome events.
Brooklyn bridge, If there is any sunny day during your trip, take a walk through this bridge.
Washington square park, ease your mind, take a seat, chill and relax.
Houston hall, nice place to grab a beer. Craft brews and bar bites.
International center of photography, must visit place if you are interested in photography.
Union square, young and vibrant atmosphere.
Bryant park, it has an ice rink during the season.
Film forum, check out the newest low-budget film.
East river, good to take a walk.
St.Patrick's cathedral, everyone needs this kind of place at least once in their life, I guess.
New York public library, great place in both architectural aspect and its atmosphere.
MET opera, oh, there is nothing to say more.