For low key, dive bars, these are my recommendations (if you want fancier, high-end stuff, I can recommend that too):
1. Lakeside Lounge - My favorite bar in NYC is the Lakeside Lounge at 11th Street and Ave B. It's got cheap booze, a photo booth, the nudie photo hunt video game, and live rock 'n' roll.
2. Hi-Fi - I also recommend Hi-Fi on Avenue A. between 10th and 11th Street. They've got this absurd digital jukebox filled with punk and rock n roll, a pool table, pinball, Big Buck Hunter, and old record covers lining every wall.
3. Black Bear Lodge - 3rd Avenue between 21st and 22nd Street. The crowd can get kind've douchey sometimes, but it's a dive bar that's themed like a lodge in the middle of ski country. Very laid back. There's a giant taxidermied bear.