Roppongi Hills

Roppongi Hills, originally uploaded by AdrielH.

Roppongi Hills is on my Tokyo 'must visit' list. It's now several years old, but still one of the top new neighborhoods in Tokyo (probably until the Sky Tree development opens in 2012). The centerpiece of Roppongi Hills is the soaring Mori Tower, and there is a beautiful Japanese garden near its base.
Before the Roppongi Hills shopping and leisure district was developed, Roppongi was known chiefly for its nightlife. It is also an embassy town, with literally dozens of foreign offices. You definitely can feel the international presence when walking around the city, especially in contrast to the homogenity of many Tokyo districts.
Roppongi is also an art mecca, with three museums, including one in the Mori Tower.