You mentioned Tokyo, Ise, Nagoya, Takayama, Kanazawa, Kyoto, Mount Koya,
Osaka, Hiroshima, Miyajima Miyajima, Nagasaki and Himeji. All of these are
cultural/historical places so you don't include nature spots. Also you plan to
stay in Tokyo for 10 days which, in my opinion, is far too long for the first
timer traveling 30 days. Of course everyone has different preferences, but
I would recommend you to do some nature trips and stay less in Tokyo. In general
staying in Tokyo cost more than staying in rural area.
I would recommend you to buy Three Star Route Shinjuku ticket.
https://www.bus-navi.com/news/d3537db208ce9dcd2aff.pdfThis combination bus ticket will take you from Shinjuku (in Tokyo) to Matsumoto, Hirayu Onsen, Takayama, Shirakawago and finally to Kanazawa or Toyama (8560 yen, valid for 7 consecutive days). If you add 2050 yen you can visit Kamikochi, the best mountain resort in Japan, from Hirayu Onsen.
Also you might consider travel to Murodo, the highest point of Tateyama Kurobe Alpine Route from Toyama (around 8000 yen round trip, you can't use Japan Rail Pass for this section). Murodo and Kamikochi are very nice place but the accommodation is rather expensive but there are some cheap options.
http://www.nishiitoya.com/en/8500 yen icluding two meals.
http://www.mikuri.com/english/index.html9300 yen including two meals.