You've heard about the reading room at the New York Public Library, haven't you? Then I need not go on. Just look at it. And you're allowed to hang around in there!
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!).
I love having Breakfast at Le Coucou - you'll find me here several times a week. Le Californien, OJ and Expresso! Dinner is very formal - but amazing if you dig the French high-end, but Pro tip: They have amazing drinks, so drop by and hang in the bar for a few drinks!