Need advise

Hi, I'll be flying with some friends to Tokyo Narita on May 17. One of my friends will be attending a congress in Tokyo and we will be able to start our tour "out "of Tokyo on May 22.
We would like to visit Hakone, Kyoto and maybe continue to Takayama and Shirakawago.
We need to go back toTokyo to fly out to Italy on May 29.
We were considering to visit also Nikko, but maybe during our stay in Tokyo.
Is it worth to buy JRP and if so, a 7 or 14 days one?
Any advise is appreciated. ciao e grazie

Melania