JUN29 NARITA AIRPORT to TOKYO Narita Express
2820yenJUN30 YUDANAKA (via new bullet train extension) It looks like it is just till Nagano on JR
8000yen Then it is a private line which is not covered.
JUL02 train to TOYAMA & then TAKAYAMA Again Yudanaka to Nagano is private line. But Nagano to Takayama is covered by JR
10130yenJUL03 Bus to SHIRAKAWA-GO Nohi bus which is NOT covered.
http://www.nouhibus.co.jp/english/shirakawago_kanazawa.htmlJUL04 Bus to KANAZAWA then train to KYOTO You can use same Nohi Bus to Kanazawa. Then Kanazawa to Kyoto on JR
6700JUL05 / JUL06 maybe one day trip from KYOTO Depends on where but I would say about 500-1200yen+
JUL07 train to OSAKA Again this could be between 560-1530yen+ depends which train you take
JUL08/09 Possible day trip NARA? SHIGA? 1600yen roundtrip to NaraJUL10 train / bus to MT KOYA Get this pass
http://www.japan-guide.com/e/e2358_012.htmlJUL11/12 train to ONOMICHI (cycling trip) Osaka to Onomichi JR
8090yenJUL13 train to OSAKA Onomichi to Osaka JR
8090yenJUL14/15 train to NAGOYA Osaka to Nagaya JR
6150yenJUL16 train to Mt FUJI (summit climb) I recommend Kawaguchiko side
http://www.japan-guide.com/e/e6906.html however starting from Nagoya you would at best arrive in the afternooncit might be better to go back to Tokyo first and then early morning start for day trip to Kawaguchiko and to 5th station. Also the summit climb could take many hours to do. Nagoya to Otsuki station
12050yen then private line to Kawaguchiko.
JUL 17/23 train to TOKYO possible day trips to GHIBLI museum, YOKOHAMA Kawaguchiko to Otsuki private line. Then Otsuki to Tokyo JR
2740yen. The rest to the trip is small fares so maybe get a Sucia IC Card here.
JUL24 Fly home from NARITAIf you start a 21 Japan rail pass from Jun 29 – Ending on Jul 19
And assuming you also go to Kawaguchiko side
Total regular tickets 62400+yen
21 day Japan Rail Pass
59350yen
It is still hard to say if that would be worth it because we do not know if you would pick the Kawaguchiko side for Mt Fuji.
Conclusion: 21 days yes if Kawaguchiko side, otherwise the Japan Rail Pass would probably NOT work out, even the 7 or 14 days. If you are flexible we could maybe work out 14day rail pass but you have said most of your hotel is booked.
Hope this help!!!
Have fun!!