Which JR pass to choose?

Hi!

Me and my boyfriend wil travel in Japan for three weeks starting September 20. As we are also planning to stay in Tokyo, Kyoto and the Japanse Alps for a few days and know that we cannot travel with a JR pass there, we are confused if a JR pass is worthwhile and if so which one to pick and when to activate.

Our itinerary is like this now:

Sept 20 - Arrival in Tokyo and travel from Narita to Tokyo Central
Sept 21 - Tokyo
Sept 22 - Tokyo - Daytrip Nikko
Sept 23 - Tokyo
Sept 24 - Tokyo
Sept 25 - Tokyo - Matsumoto - Kamikochi
Sept 26 - Kamikochi - Takayama
Sept 27 - Takayama
Sept 28 - Takayama - Shirakawago - Kyoto
Sept 29 - Kyoto
Sept 30 - Kyoto
Oct 1 - Kyoto - Daytrip Nara
Oct 2 - Kyoto
Oct 3 - Kyoto - Koya San
Oct 4 - Koya San - Hiroshima
Oct 5 - Hiroshima
Oct 6 - Hiroshima - trip to Miyajima
Oct 7 - Hiroshima - Osaka
Oct 8 - Osaka
Oct 9 - Osaka to airport

Thanks in advance for your feedback!