Thankful for your input

Hello,

We have a 14-day JR pass and 18 days in Japan. We thought to activate the pass at the airport and use it to travel from airport to Tokyo. Is it useful within Tokyo? We fly out of Kansei and will end our trip in Kyoto. I thought just to take a taxi to airport from Kyoto...

I follow with more questions:

We have a plan sketched out and would be happy for your input:
Days 1-3-Tokyo 3 days
Day 4-Daytrip to Kamakura and continue to Kawaguchi-ko (is this possible? not too long a day? do we have to go back through Tokyo?)
Day 5-Day at Fuji
Day 6-Travel to Japanese Alps:
We would like to see Takayama, Walk in Kamikochi region, Shirakowa-Go, Nagano, Matsumoto, Maybe walk from Magome to Tsumago...) How can we travel around the area and connect the different valleys? Should we rent a car and drop in a different place? We would spend 4 days, so we know we must cut out something...
Do we have to travel through Nagoya both ways to/from Japanese Alps?
Day 11-Travel to Nara and Kii Peninsula for Kumano Kodo (just two days) and maybe Koya san.
Day 14-Travel to Kyoto