There are many great bars/pubs in Tokyo but Ishinohana in Shibuya and Bar HiFive in Ginza are one of the most famous bars. Their cocktails are really amazing and creative.
New York Bar in Park Hyatt Shinjuku is also very famous. It was used in the film Lost In Translation. Nice atmosphere and great cocktail, great service, great views!
Lately, many travelers go to Golden Gai to search for good bars. The Shinjuku Sancho-me area close to Golden Gai have many great bars as well.