Indeed, being from NYC, most of the suggestions here are excellent "tourist" destinations. Off the top of my mind (in no particular order):
-Empire State Building (or the Top of the Rock at Rockefeller Plaza)
-Statue of Liberty
-Ground Zero
-Rockefeller Center
-Times Square
-Fifth Avenue
-Chinatown, Little Italy, and SoHo (Chinatown's Canal Street is a must

)
-Central Park
-South Street Seaport
-Those double-decker buses that scream "I'm a tourist!"
Want the best bagels (IMO) in NYC? H&H Midtown Bagels East. Period, end of story.
http://www.hhmidtownbagelseast.com/
It'll also give you a chance (time permitting, of course) to venture into the Upper East Side.
As for activities, if you're the type and have the budget, Broadway Shows are always memorable and fun (I think that strike is now over?). I guarantee, you'll have a ton of fun in the city no matter what you ultimately decide to do. Have fun!
Oh, I see you're from Southern California (I'm currently studying at USC). I'm assuming this is going to be your first time to NYC, so if necessary, be prepared for a weather shock. Bring plenty of warm clothing and such (apparently last week it was really cold, but it's currently not as bad). For me, it's kind of odd wearing flip-flops in December right now...