Some cool things to do in Japan:
1. Go to a Karaoke club and sing all night.
2. Go to a Sumo tournament (held six times a year throughout Japan.)
3. Climb Mt. Fuji (best from June through September).
4. Go to an Onsen (hot spring) in Kyushu.
5. See as many temples and shrines as you can in Koto and Nara.
6. Go skiing or snowboarding in Hokkaido.
Some weird things to do? That depends on you, but...
1. Try to sample some of the exotic food (whale meat, raw blowfish, BBQ sparrow...)
2. Visit the Monkey Mountain in Beppu and hang out with the monkeys.
3. Stay in a "Love Hotel" which, can be paid for by the hour, or overnight.
4. Have a cup of coffee in a "Maid Cafe" where all the waitresses are dresses as maids.
5. Stay in a "Capsule Hotel" where you get to sleep in a small box like capsule. Cheap!
6. Go to the "Tsukiji Fish Market" where you can see the most expensive fish in the world being traded in auction madness. Need to be there really early in the morning, like 4:00 am. over 4 years ago