Roppongi - Where to go

The main attraction in Roppongi is of cause Roppongi Hills so don't miss the Roppongi Hills tour which will introduce you to this area of Tokyo.
Although Roppongi is cataloged as an entertainment area, don't forget that you are in Japan, so even here you can find a nice little temple.

See more on these posts:

Roppongi Hills Tour
Senshouji Temple

You can also visit few art museums that are located in this area:

Roppongi Museums