7/14? + Koyasan

Dear JR team,
Please help me decide what JR pass I should buy and what's the best way how to get to Koya San ;)

I am arriving to Narita 15.11.
I am gonna be in Tokyo till 22.11.
I do plan some days trips though
(Nikko for sure, Maybe Kamakura and Yokohama) + probably using the monorail and metro if needed

Going to Kyoto 22.11.
To Nara 24.11.
To Koyasan 25.11.

Then 27.11. Back to Tokyo and then back to Amsterdam at 29.11.

I would like to know if I should buy 14 or 7 days JR pass to only cover trip to Kansai
+ I am traveling to Koyasan from Nara and there seemes to be only transport where JR pass cannot be used.
May you give me advise?