Which pass for 15 day trip?

Hi

I think we can just use a 7 day pass for the following itinerary but would like to check
5 nights Kyoto
2 nights Hiroshima
1 night Nagona
2 nights Takayama
5 nights Tokyo

I thought we would activate the pass on the day we go to Hiroshima as we I assume we would not need it for Kyoto or Tokyo as it would be cheaper to pay for those cities as we need it.
Does that make sense and does the itinerary look ok?
We may also go to Hakone but have not decided yet

Thanks for your help

Robyn