The best part of the new Whitney Museum is the view in all directions from the terrace - and also from the staircase facing West. I'm afraid it upstages the Art.
Another Gramercy all-star, I really like this place, you need a reservation or early arrival, sitting in the bar is always fun and the food is amazing!
If you're far up in Greenpoint and need caffeine + snack, Bakeri is my spot (I say "bake-ery", others say "bach-ery"—I still vote the former). Known for their baked goods—both savory and sweet—it's the perfect spot for a coffee meeting, small breakfast, or a solo book read. There's one large communal table in the center, plus a few two-tops and decent counter space—one of the rare cafes with enough room that it's rarely packed (except saturday!).