First Trip to Japan

Hello,

First tip to Japan this year, planning to go from end of September through October for just over 3 weeks. Itinerary at the moment is roughly as follows:

Tokyo 5 nights (day trip to FujiKawaguchiko)
Matsumoto 2 nights
Takayama 2 nights
Kanazawa 2 nights
Kyoto 4 nights (day trip to Nara)
Hiroshima 3 nights (visiting Himeji on the way, and day trip to Miyajima)
Osaka 2 nights
Hakone 2 nights
Back to Tokyo

I may need to reduce by one day, thinking either Matsumoto or Hakone are likely to go down to one night- any advice on which would be better to spend more time in and around appreciated.

Difficulty is also working out trains and buses between the destinations. Whether a JR pass is now worth the extra cost, or all of the individual type of rail passes and then what they actually cover! Think I will need to get a few buses as well. Is it a risk turning up on the day for transport in Japan? Or should I look to prebook where possible?

An hints or trips on travel and this itinerary would be greatly appreciated. Thank you.