14 Days in Japan (do I need JR pass)?

Hello,

I'm hoping you could help me to figur it out what is the more efficient way to go from:

a) Koyasan to Tokyo?

b) Koyasan via Hakone to Tokyo?
c) Koyasan via Takayama to Tokyo?

d) Kyoto to Yamazaki distillery?

The rest of my itinerary: We arrive and depart in/from Tokyo Narita (20.11-04.12).

Tokyo-Kyoto (sleep)

Kyoto (5 full days), with a day trip to Nara and to Yamazaki

Kyoto- Koyasan (sleep

Koyasan - ?? Osaka ? (sleep) or soemthing closer to Tokyo, but maybe within the Alps? - not sure how to way back to Tokyo, what to chose "in between"?

Tokyo (4 full days), with a 1 day trip to Fuji Lake.

Regardless the points b)->c) - I am searching a place "on the way", different from Kyoto and Tokyo, so to have different expierience, but not sure, if I have time for it?
Or maybe to much effort and just to add an extra night in Tokyo instead?

Would it be a Japan Rail Pass a good option for my plan?

Thank you so much for your help!