JR Pass suitable for itinerary

Hi,

We are travelling in Japan for 17 days in April.

Our plan is to arrive in Tokyo, and stay in the city for 4 nights.
We are then moving onto Kyoto for 4 nights.
Next we are spending 2 nights in Hiroshima, before spending 1 night on Miyajima.
Finally, we are going back to Tokyo for a further 4 nights.

Whilst in Tokyo, we plan to take day trips to Kamakura and possibly Nikko.
Whist in Kyoto we would like to visit Nara, and possibly Ise or Kurama.

We are thinking our best option would be to purchase a 14-day JR Pass.
Would you agree?

Are there any of our planned journeys where we would not be able to use the pass?

Thanks for your help.