Hi there,
I would recommend the following itinerary since in this way, you will need to take a bus only for Kawaguchiko to Kofu, Matsumoto to Takayama, and Takayama to Shirakawago/Shirakawago to Takayama. You can just use Japan Rail Pass (JR Pass) for the rest of routes.
[Day 1] Narita > Shinjuku > Kawaguchiko
[Day 2] AM: Sightseeing Kawaguchiko
2 PM: Leave Kawaguchiko > Kofu >Matsumoto
[Day 3] AM: Matsumoto Castle
3 PM: Leave Matsumoto Castle >Takayama
[Day 4] Sightseeing Takayama/Shirakawago
[Day 5] AM: Leave Takayama > Nagoya > Kyoto or Osaka
[Day 6&7] Sightseeing Kyoto/Osaka/Nara
[Day 8] Leave Kyoto or Osaka for Tokyo
[Day 9] Tokyo
[Day 10] Tokyo > Narita Airport