Here is my itinerary, i would like to use Shinkansen as much as possible and my first train trip will be June 29 (Tokyo - Mt Fuji) and my final train trip will be July 7 (Kyoto - Tokyo)
TOKYO (SHUBUYA) - MT FUJI (with a guided hiking company)
MT FUJI - HAKONE (taxi may be better?)
HAKONE - OSAKA
OSAKA - NAOSHIMA (day trip, may be with a guided tour company)
NAOSHIMA - KYOTO
KYOTO - TOKYO