I am with jib71.

I suggest moving your trip from Tokyo-Kyoto one day to June 23. Then activate your Rail Passes for June 23-29. Go to the Ghibli Museum earlier in your stay in Tokyo.

During the 7 days of your Rail Pass, you can use it for the round trip Tokyo-Kyoto-Tokyo, day trips in and around Kansai (Nara, Osaka by shinkansen, Hikone and other great day trips, perhaps even down to Okayama or Kurashiki) and the Narita Express back out to NRT to depart on the 29th. The Pass won't really pay for itself if you only use it for the round trip Tokyo-Kyoto-Tokyo but WILL pay if you add in those other trips. Use the Narita Express+Suica pass to get into Tokyo from NRT upon arrival and to get around Tokyo on the subways and local JR trains.

June tends to be typhoon season so be prepared for rain and possible weather-related changes of plans.