Hey Minh,
Well, lucky you! Japan is a real treat in so many ways, and it is a very lovely country in which to cycle. Where will you be going and how long will you be in Japan? Will you have your bicycle with you?
If you can get to Kyoto then I'd suggest a late-night cycle tour through the Gion district. In addition, an early morning cycle tour of the 'Five Mountains'- the five main Buddhist temples of Kyoto- was something I very much enjoyed doing.
If you get to Kyushu, and find yourself in Kagoshima, there's a really great ride around Sakurajima- a very active volcano a short ferry away.
There's a million things around Tokyo (not helpful, I know), but you'll be there at a very beautiful time of year weatherwise. Hakone is a cool day-trip where you can hike, enjoy a beautiful outdoor sculpture museum and indoor Picasso exhibit, and dine at the Gora Brewery- a Nobu restaurant.
As you may have read in Will K's musings on Tokyo, it is a wonderful city in which to ride a bicycle.
Enjoy! John