Advice needed on (length of) JR pass

Hello!

Brief check made us unsure whether we need the JR pass or not and if so, how long (14 or 21 days). Some advice would be welcome!

Our schedule:
Day 1: Arrival in Kansai Airport - 1 night in Osaka
Day 2: From Osaka to Koyasan
Day 3: From Koyasan to Kyoto with a trip to Nara on the way
Day 4 - 5: Kyoto
Day 6: From Kyoto to Matsumoto
Day 7: From Matsumoto to Nagiso
Day 8: Bus to Magome (we stay two nights in Nagiso)
Day 9: Train and bus to Hakone (we stay at Moto Hakone and will use ferry / local bus)
Day 10: From Hakone to Shirahama
Day 11: Day trip somewhere on Izu peninsula
Day12: From Shirahama to Nikko
Day 13: From Nikko to Tokyo
Day 14 - 17: Tokyo (local transport + for ex. Kamakura)
Day 18: Tokyo to the airport :(

Thanks for the feedback!