what to do depends a lot on your interests. here are some of my suggestions assuming Tokyo the whole time:
Asakusa, Sensoji (Buddhist temple) lots of traditional (or faux traditional) goods in the shops leading up to the temple. Popular tourist spot for visitors from everywhere, foreign and domestic.
Tokyo Metropolitan Photography Museum.
https://en.wikipedia.org/wiki/Tokyo_Metropolitan_Museum_of_Photography
Nihon Minka-en Japan Open Air Folk House Museum.
http://english.nihonminkaen.jp/
Check out a Shinjuku or Akihabara camera store. Yodobashi is a good one.
Akihabara, the "electronics town" is fun to just wander around and look at the shops.
Good day trips include Kamakura, the site of the giant Buddha from some time in the 1400s (if not earlier), and Nara the site of Tokugawa Ieyasu's tomb, the Shogun who unified Japan in the early 1600s, and started the system of government that lasted until the 1860s.
A decent half day trip is take the Keio train line to Takao and ride the funicular railway to the top of the mountain. Or walk, it's not a huge climb.
Walk and explore. Go to a department store and check out every floor. Take the subway or train out to the 'burbs and walk around there. See how the more ordinary Japanese live.
