I'll strongly second the recommendation for Dram. Really great spot for quality cocktails, and plenty of restaurants nearby.
Brouwerij Lane is a nifty little Greenpoint beer store/bar with impressive taps and a friendly, informative staff. It'd be good for a stop on a bike ride, but isn't the kind of place I'd lounge for hours.
Strong Place is a beer bar in Cobble Hill with an Avec feel (but not the crowds) and some good looking food. We stopped there for a drink during our wait for a table at Mile End and almost had dinner at Strong Place instead, the food looked so tempting.
Closer to Bushwick than many corners of Brooklyn, PIGMON and Trixie-Pea recently turned us onto Dutch Kills in Queens. It's a very cozy, high quality cocktail bar, and there was a live pianist during our visit. The bartender and the crowd were a lot of fun.
Oh, and if you're staying in Bushwick, I'm guessing you're already familiar with Roberta's. While not a bar, they serve alcohol and would be at the top of my list.
Ronna