Travel Help!!!

Hi, Me and my son will be visiting Japan between June 13th and June 27th, whilst their we will be visiting:

Tokyo - 13/06 - 16/06
Kyoto - 16/06 - 19/06
Osaka - 19/06 - 22/06 (Hiroshima for day trip from Osaka (20/06))
Tokyo - 22/06 - 27/06 (Chuzenji - 23/06 - 24/06 (driving and staying 1 night))

We plan on buying the 7 day JR Pass for the dates 16/06 - 22/06 which should cover our travel from Tokyo to Kyoto, Osaka and Hiroshima and back to Tokyo. Would this pass cover bullet trains for these journeys?

Is this the best way to travel to these places in Japan? Is their a better option?

Any help would be appreciated.

thank you

Iain