Okay, I've lived in NYC and Westchester all my life.
>>1143225^this is nice starter advice. I personally hate Times Square but the scale and experience are pretty unique, and I could see it being worth it for tourists.
The Met really is one of the best museums in the world, because there's so much variety and you could spend an afternoon there without seeing the whole thing. I personally love the musical instruments wing, which is tucked away from most of the other exhibits.
Central Park is iconic for a reason; go there for a few hours.
I don't know what the best pizza is these days, but you'd be stupid not to eat some because we're famous for it.
As others have said, there are many directions your trip can take. Personally, I'd focus on two things if you want to really get to know NYC outside of the tourist bubble: exploring a few choice neighborhoods on foot, and eating food you wouldn't experience elsewhere.
Personally I'm a sucker for Greenwich Village at night, partly because I'm an NYU grad. Check out the newly reopened Pommes Frites for some really good fries and sauces, and wander around the West Village at night while you eat them. Or if you're in the east village, Odessa and Veselka are always solid.
Chelsea is great too -- if it's nice out, walk along the Highline. If it's raining, Chelsea Market is really cool and fucking huge.
Halal street food is famous and worth trying if you're into that. The most popular cart is the Halal Guys on 53rd and 6th, and it's significantly better than most of the other Halal carts in NYC. I'm also fond of King of Falafel in Astoria, though I'm a few years behind and there may be new carts that are even better.
You may be tempted to visit Brooklyn. I'd start with Williamsburg and Greenpoint for the Polish food (yeah yeah hipster whatever). Fort Greene and the area north of Prospect Park are also beautiful, as is the park itself (and the botanic gardens there).
I'm open to questions if you like.
