Shibuya is most famous for the intersection crossing near the train station. Every minute or so all pedestrian crosswalk lights turn green and shoppers, commuters, and diners dodge one another as they try to reach the other side before the light turns red. It's another one of Tokyo's must see events up there with the Tsukiji Market tuna auction - fortunately this doesn't require a 3am wakeup.
The streets that radiate out from this crossing have shopping and dining catering to a younger crowd and lots of tourists seem to make Shibuya their base for exploring the city. Once you've videotaped the crossing from above the next step is to brave the mayhem and cross the street yourself then tuck away into a restaurant or cafe.
EBISU - DAIKANYAMA
When exploring Tokyo for ten days you inventively begin to wonder where the Soho, Greenwich Village, etc. areas are - as you rotate between the major train station hubs the shopping, restaurants, and street life of each hub begins to blend together. What makes New York, New York, is these small great neighborhoods and they can't be found anywhere else including Tokyo. Tokyo does have two similar sections: Daikanyama and Shimokitazawa. Daikayama is accessible from the Ebisu JR / Metro Station. Ebisu has a few restaurants along a block north from the station but further west is the slightly hipper Daikayama. Daikayama has many cafes, coffee shops, and boutique clothing stores that give the neighborhood a cool but not quite pretentious feel. Shimokitazawa further north has a similar feel. If you are looking for a weekend brunch then lazily go cafe hopping these two smaller neighborhoods would be the place.
HARAJUKU - OMOTESANDO
On Sunday's Harajuku and nearby Yoyogi Park attract a lot of youth who dress in costumes. There's a street with second hand and vintage clothes that for some reason is a must have photo for tourists. On the opposite end of Harajuku from Yoyogi Park is Omotesando - supposedly Tokyo's Champs-Elysees - other than high end retail and a few cafes it's a wayward comparison.
The third point of a triangle with Shibuya and Harajuku is Roppingi an upmarket area with nightlife comparable to Ginza. The recently opened Roppingi Hill's is an affluent lifestyle mall where Tokyo's wealthy go to flaunt their style.