- Museum of Modern Art (MOMA) or The Met. The Met is great, but if you just do one museum I'd say MOMA. I felt like you got more recognizable art/artists in a smaller space and it's not as overwhelming as The Met.
- Walk around Central Park
- Walk the High Line
- Walk across the Brooklyn Bridge, then walk around Brooklyn Heights
Food (you probably can't go wrong with almost any recommended food) - Katz's Deli - Joe's Shanghai (Chinatown) - Veselka (Ukranian Deli for pierogis in East Village) - Levain Bakery (Chocolate Chip cookies) - Momofuku - L'industrie Pizzeria (West Village)- hyped up by-the-slice place that may or may not have a long line.
We went a few months ago for 5 days, but mostly hung out the East Village area. So i have a bunch more recommendations for that area