First, I would be interested to know at what time of the year you will be traveling, because this could impact different seasonal sights or festivals you might want to see.
Second, I would like to know if you have been to Japan before, and if you have, where you have been. For right now, I'll assume you haven't been there, because it seems like you haven't.
My major suggestion would be to extend your stay in a few of the places where you are only spending one or two days in.
After day 7, I would spend at least one more full day in Osaka. I would also spend one more full day (with a night there) in Hiroshima. I would also spend an extra day in Nagasaki, and possibly a day or two more visiting another place in Kyushu, like one of the volcanoes (Kirishima National Park or Mount Aso) or Beppu hot springs.
I would also spend at least two more full days in Tokyo (for a total of four, not including the side trips). Tokyo is such a large and fun place. You will not run out of things to do in Tokyo.
Another possible place to take a day trip from Tokyo, is Fuji Five Lakes, to see Mt. Fuji and visit the neat lava tube caves (Bat Cave, Wind Cave, and Ice Cave). If you are in Tokyo for about a week, you could keep an eye on the weather forecast (checking online) and go there on a day when it is clear.
You should also extend your stay in Kanazawa by a day, and maybe another day in either Takayama or Nagoya.
As for possible other suggestions, I would try to do more than just see touristy spots. Visit an onsen, rent a bike and ride around in different places where most tourists don't go, see a baseball game, see a concert, go to a festival, try the local food specialties, go to a private room Karaoke place, like Shidax, go to an arcade place, like Leisureland, go to a batting cage or bowling alley, visit a an outdoor market, go hiking somewhere where tourists don't always go. You will enjoy these more authentic experiences, because they will be unique and memorable experiences.
As for other places to visit, I would recommend renting a bike and biking in the Seto Inland Sea:
http://www.japantravelinfo.com/blog/?p=1006Another place to spend a day at could be Kobe, a beautiful seaside city. I enjoyed the Earthquake Museum and Akishi Kaikyo bridge area.
Another idea would be to choose a town or city that is accessible by train near a place where you will be staying that is not a tourist spot and that is out in an agricultural area. Stay there for a couple days and rent a bike and see what it is like to live in Japan for non-big city people. Relax, and visit shops, parks, stores, restaurants, arcades, bike in suburbs and agricultural areas, etc, and see what life is like for these people. I did this when I stayed with a friend who taught English in Isesaki, in Gunma Prefecture. It was a lot of fun and very interesting.
As far as logistics go, you would need to buy a 3 week JR pass obviously. But since you are staying a month, you would not want the pass to be activated until you head to Hiroshima and Kyushu and then up to Tokyo (after traveling in Kyoto, Osaka, Nara, and Mount Koya).
I would recommend buying multiple Japan travel books and reading up on them. I liked Lonely Planet Japan, Frommer's Japan, Time Out Tokyo, Lonely Planet Hiking In Japan, Exploring Kyoto, Japan Atlas: A Bilingual Guide, Tokyo City Atlas: A Bilingual Guide, Streetwise Tokyo map, and Day Walks Near Tokyo. You should also familiarize yourself with all the train routes on JR websites. And use this site for train schdules:
http://grace.hyperdia.com/cgi-english/hyperWeb.cgiHope this helps. Let me know when you are going and if you have been to Japan before. Have fun planning!
