1 month excursion - jr pass

Hi,
My girlfriend and I are planning to go to japan in september for 1 month.
We would like to take the JR pass for 21 days since we are staying 9 days in tokyo at the beginning so we'll not use the JR pass.
Here is the rest of our excursion :
Tokyo - Kamakura - Kawaguchiko - Nagoya - Kyoto - Osaka - Hiroshima - Tokyo.
Is it worth it to take the jr pass for 21 days ?
With this itinerary, can we use only the JR pass (train or buses). If yes, which trains and buses do we need to take ?
Are we going to need to pay additional fees for some routes ?

Thanks in advance,