Only place I can think of by name is Gas Panic in Shibuya, there's one in Ropponngi as well. It's a Reggae / Hip Hop bar. We went on a weekday and the place was packed. I know they had more than one beer on tap and bottles, don't remember the price cuz I was pretty drunk by the time we got there. Good mix of people. The place was kind of on the small side.
GASPANIC
My favorite bar in Japan is in Osaka
http://www.rockrock.co.jp/
Reptiles have silly grins
Dark eyes--shiny teeth--some have fins
Samurai they smile never
Serious--pretty swords--very clever