I think Uji has a pretty good list and mine wouldn't differ too much. This is not in a specific order but I will say:
1. Visit Tokyo - Too much to list. You could just stay here and still not scratch the surface but start with Yakitori under the train tracks at Yurakucho, go to an Izakaya in a businessy type area for dinner, Harajuku/Omotesando, Shibuya, Shinjuku, Akihabara, eat at one of the MANY Michelin starred restaurants or find a b-gourmet blog and follow their restaurant suggestions for the cheapy version.
2. Kyoto - specifically: Kinkaku-ji, Ginkaku-ji, Kiyomizu-dera, Ryoan-ji, Gion, Sanjusangen-do, Koko-dera and Toei studio park for its cheesyness
3. Miyajima & Hiroshima
4. Stay in a Ryokan
5. Stay in a love hotel v- a really odd and out there one. These are pretty easy to fin and it's not as seedy as it sounds. Try Love Hotel Hill in Shibuya.
6. See the Cherry Blossoms but get involved with the drunken, karaoke singing locals in the park.
7. Ride the Shinkansen and make sure to get your eki-ben.
8. Visit one or many them parks
9. Eat at a street food stall (The yakitori in Yurakucho counts but is not quite the same). You will see them pop up, particularly around the stations just before evening.
10. Go to a festival or 10. They are often very interesting and a lot of fun. Have a look at this thread for some suggestions
http://www.japan-guide.com/forum/quereadisplay.html?0+99544 Just get lost in the back streets, back towns and wander around. I found the most wonderful and weird things doing this.
You could come up with a list of another 10 things that are completely different to this and I would probably agree that it is equally as good and worthwhile.