Tokyo - Kyoto - Hiroshima - Sapporo

Hi!

We've almost completed our itinerary, well, we know where we want to go and what we want to see, now we just need your expertise to help us with the itinerary to make sure it is logical and will make best-use of a rail pass and time.

Any assistance/advise would be appreciated.

We'd like to:
Stay in a temple at Koyasan
Stay in a Ryokan at Miyajima

Questions:
We'd love to visit Akita but not sure it is worth the trip from Tokyo, unless we could stop at Akita on the way to Sapporo - Any tips on this would be appreciated.
The items with "JR" I believe are covered by the JR rail pass, other trains (Kyoto <-> Koyasan) are not; is this correct?
Are there other day-trips or places we could stop on the way, to make use of our rail pass and see other cities between major destinations?

Itinerary:
1 Tokyo
2 Tokyo
3 Kyoto (from Tokyo by Train) JR
4 Kyoto
5 Koyasan (via Osaka, from Kyoto by Train)
6 Kyoto (via Osaka, from Koyasan by Train)
7 Hiroshima (from Kyoto by Train) JR
8 Hiroshima
9 Miyajima (from Hiroshima by Train & Ferry) JR
10 Sapporo (from Hiroshima by Plane)

Thanks in advance for your assistance.

Kiapso