I did a 39 day trip back in 2012, so I have a rough idea of how you might be able to organize your trip to save travelling costs. My suggestions:
1) Start off in Hokkaido if you can. Perhaps you can transfer at Narita and make use of the 10,800 yen discounted flights from JAL or ANA. If you go early enough, you may be able to experience some winter festivities going around. The Sapporo Snow Festival is going from the 5th to the 11th of February, and the Otaru Snow Light Parth is from the 5th to the 14th of February (very good for photos). Even without the festivals, you can easily spend 5 days just exploring Sapporo and Otaru. I know there are glass making classes in Otaru if you are interested.
2) Fly down to Kansai, making us of another 10,800 yen discounted ticket. You can easily spend 10 days exploring Kyoto, Osaka, Kobe, Nara, and Mount Koya, if not more! Temple lodgings are an experience. You can mix up temple days and city life so that you don't get too tired of temples.
3) Activate a JR National 21-day Pass, and just explore. Recommendations are Hiroshima, Miyajima, Fukuoka, Nagasaki, Kumamoto, Kanazawa, Takayama, Nagano, Matsumoto. You may also revisit the Kansai region if there are any festivals ongoing, such as Omizutori in Nara or Hanatoro in Kyoto. You may also want to use buses in between where places of interest cannot be access by trains, such as Kurokawa Onsen, Shirakawa-go, and so on.
4) Make sure to end up in the Kanto region (i.e. Tokyo). If you have any time left on your pass, you can make a daytrip to Nikko. You can easily spend 6 days exploring Tokyo, Kamakura, and Yokohama. If you are lucky, you may encounter a wedding at Meiji Shrine.
That alone would be 42 days worth of travelling :) If you are entering and exiting through Kansai instead, then just rearrange (2) and (4).
Check out the following for a list of decent Japanese gardens:
http://www.japan-guide.com/e/e2099.htmlIf you want to find out things you can do and experience, I also suggest checking out the Wikitravel entries for some of those places I listed. They often have recommendations for things to do. For example, the Kyoto entry has listed some temples where you can participate in a Buddhist meditation session if you are okay with trying it out.