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!).
Roll N Roaster is a fast food place in Sheepshead Bay that has been open since 1971. Get the roast beef sandwich with cheese and a bottle of Moet champagne (not joking).
The permanent piece called "Meeting" at MoMA PS1 is an etherial experience of light and color and quiet. Sit and look through the cutout in the ceiling and watch the light change both outside and in. You can't tell what you're looking at until maybe a bird flies by.
I'm a huge Japanophile: if there's one other place I'd like to live, it's Tokyo. I must have been there seven or eight times, most recently just after the Tohoku earthquake and tsunami. Anyway, EN is a gem on Hudson Street, serving real Japanese cuisine. It turns out that EN is a chain in Japan; there are a lot of branches making lovely bosky food in cosy neighbourhood locations. But their New York incarnation is grand in scale and ambition, with solid, warm interiors (not unlike if the Whitney were a Japanese restaurant, oddly) - a remarkable hybrid of this city, and the other one that I'd love to live in.