You can't say you've seen NYC until you've seen it from a boat. Hop on the ferry from anywhere to anywhere and you'll see what I mean. Not only will you see excellent old buildings and factories--the inner workings of the old industrial city--but you'll head out under working bridges and see the skyscrapers in all their towering glory. And once you've done it, do it again, at night.
My favorite Chinese food spot. The best Peking duck! Ignore the C health code rating in the window, they must have made a mistake ;) Also, It's BYOB with no uncorking fee, go crazy.
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!).
This artist-run gallery is a hub of the Brooklyn gallery scene. You'll find Bungee, a celebrated fixture, snoozing comfortably in the office and somehow oblivious to all the surrounding chaos.