Shibuya
Shibuya is one of the most wicked area in Tokyo. Many Japasene youngsters, school kids hang out there. Don't miss the pedestrian crossing at the JR Hachiko exit that was seen in the film "Lost in translation." Apparently, it is the busiest intersection in the world!! How about observing the people crossing there from the Starbucks with a cup of coffee on the 2nd floor?
Also it's a good place for shopping. There are lots of department stores ( Parco, Tokyu Hands and Seibu ) and shops which you can get fashionable and unique clothes.