There are tremendous bars in Tokyo, here are my recommendations:
- For fun
JBS Shibuya: http://www.geocities.co.jp/MusicHall/3707/jbs.html
Great music and casual atmosphere. Vinyls of jazz, blues, and soul.
- For delicious cocktails
Bar Ishinohana: http://ishinohana.com/en/
The bartender is an award-winning man. Their cocktail is luxury and delicious. Try the matcha cocktail called Oribe. It should be something unique in Japan.
Both of the bars are in Shibuya and open late.