Shōjō Izakaya is a pretty good place for beers, cocktails, and snacks. Been there twice, and the food's great. Try the steamed clams if you can - they are deliciously sweet when dipped in soy sauce.
It's in the basement of that little building housing the Wilfred's restaurant (which is closed for dine-in, but Shōjō is open) in the far west end of the Brewery District. Easy to spot even at night due to the string lighting in the courtyard.