Hike Mt Fuji.
What you do is, when you get there, buy a wooden staff. As you hike up the mountain there are various stations where you get a mark branded on your staff (yes.... you pay money, but it is worth it I think... and it's proof you climbed all the way).
Anyway, you arrange it where to go most of the way up. Spend the night (not the greatest of accommodations, but its only one night), get up before sunrise, climb the rest of the way, watch the sunrise from the top of Mt Fuji.
Its a must!!!
Ok... after that: Tokyo is cool, Yokohama has a big tower... but if you are limited in time, I would push for Osaka & Kyoto, both have festivals that are worth going to.
If you have time Kamakura isn't too far from Tokyo & Yokohama and has this huge buddha...you can walk inside...
etc...
Your list is definitely on track.