Travelling to Japan from Bangalore, India on 28th May

Hi there,

Our itinerary stands as below

Tokyo 28th - 2nd June
We leave on 2nd June at around 9am to Kyoto
We spend 2-4th June in Kyoto and leave 5th morning to Osaka
We spend 5th and 6th in Osaka
Do a day trip to Hiroshima on the 7th
Leave Osaka on 8th morning to Odawara and stay at Hakone
Leave Hakone on 9th morning to Shinjuku.

Considering the above, we might end up using JR Pass from 2nd June to 9th June (not sure if its useful on the 9th). We wanted to understand if it makes sense to buy a JR pass given this. For ease of understanding, we would be boarding the Shinkansen in the below routes for

Tokyo -> Kyoto
Kyoto -> Nara
Nara -> Osaka
Osaka -> Hiroshima
Hiroshima -> Osaka
Osaka -> Odawara
Odawara -> Osaka (if permitted on the 9th June in the morning given we activate our card on 2nd June at 9am)

Thanks in advance!