Roppongi is simultaneously one of the most loved and hated neighbourhoods in Tokyo. While home to the Japanese head offices of foreign companies like Google, Credit Suisse and Goldman Sachs and some of the best restaurants around, it also has a seedy reputation with a profusion of hostess bars, strip clubs and nightclubs. The sheer volume of places means there are plenty of cheapo options. The Gindaco branch located near Roppongi crossing is a good place to start.
Another claim to fame is the so called Roppongi Art Triangle – The National Art Center Tokyo, the Suntory Museum at Tokyo Midtown and Mori Museum at Roppongi Hills are all located within easy walking distance.
Additionally, there is are always free events or attractions on at either Tokyo Midtown or Roppongi Hills. Check the Tokyo Cheapo Weekend for the latest events.