Serendipity. It's a beautiful ice scream / dessert parlor. Two stories. Lovely interior. It's wonderful and dreamy and creamy and delicious.
The Metropolitan Museum of Art is a must if you're doing the museum thing. There are tons of wonderful museums in NYC, but that's really the one to go to if you're only gonna go to one.
Anywhere in Central Park.
The Lower East side, for history, for amazing Chinese food, for dive bars or swanky bars, for color and life and fun; it has a bit of everything.
Gotta stand before the Brooklyn Bridge, at least once.
Angelika's Kitchen on 12th street (off of 2nd, I think) if you like vegan food.
6th street if you like Indian food.
Williamsburg, first stop off the L train in Brooklyn, has a lot of fun shops and eateries.
Coney Island, and it's a nice ride on the F train to get there.
Have fun!
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