[Sangetsu]

Roppongi Hills and Roppongi are located right next to each other, but they are different worlds. I like the Outback steakhouse in Roppongi, and Zest Cantina, but those are the only reasons I go there.

Near Roppongi is the Midtown shopping center. It's a wonderful place to buy traditional Japanese gifts (rather than the Chinese made Japanese gifts which you'll find at Asakusa), but it's an expensive place, bring a platinum credit card.

Henbaka mentioned Harajuku. Some think Harajuku is wonderful, while others think it symbolizes all that is wrong with modern Japan. But it's good to see for yourself. There is also a Puma outlet there which can custom make a pair of shoes for you; they make a good souvenir of Japan, and the sneaker freaks will be in awe of you.