If you decide to rent or buy a bike and do some riding, get some travelers insurance first. Cyclists colliding with pedestrians, automobiles and other cyclists are frequent occurrences there. It's happened to me, personally - and things got rather complicated.
Also, if you're staying in the Kanto region and you like ramen, try to visit Kyushu Jangara in Akihabara or Ramen Jiro in Ikebukuro. You could also take the Nozomi Shinkansen out of Tokyo station, go to Shin Yokohama and visit the Raumen Bijutsukan (the Ramen Museum).
Kansai Scene cycling terms in Japanese