As
@mdchachi writes, without knowing your tastes, it's hard to make recommendations, but...
In Tokyo, you can go to Shibuya and Akihabara, the most popular images of Tokyo. Next to Tokyo is Yokohama, which has a famous Chinatown. Next to that is the Daibuttsu in Kamakura, possibly the most famous Japanese image other than Mt. Fuji. There's a year of stuff to do in Tokyo, so just going from neighborhood to neighborhood is a fun experience.
After two days, head to Kansai, where Kobe, Nara, Kyoto, and Osaka are near each other. Kyoto is good for two or three days of 'quiet' Japan. Nara is also very serene, and less touristy than Kyoto. Then finish off in Osaka, which is a more party-like version of Tokyo.