Looks like a great trip! A few points: Koyasan: You mention the bus both coming and going from Koyasan. It's pretty easy to walk everywhere on Koyasan, though you can take the bus to save time. If you do, it'll only be for a few stops, maybe a 5 minute bus ride. It's hardly worth mentioning.
The cable car fare is included in the train fare, and that takes you to the top of the mountain, which is the hard part. Walking around on the plateau isn't very hard. Be sure to visit Okunoin cemetery while you're there (early morning with the rising sun streaming through the trees is best, IMO)!
Also, when you go to Takayama, see if you can find the time to visit the Hida Folk Village.
Have you booked places to stay in each night? Most places you can just walk around and find a place without reservations, but it can be very hard to find a place to stay on Miyajima Island itself... most people stay in Hiroshima and take the ferry across just to visit Miyajima.
And I don't recall a hotel in Kamikochi, though it has been many years and my memory of the surrounding area is fuzzy (and they may have built some places to stay in the past decade too). But I left Takayama early in the morning by bus, hiked in Kamikochi all day, and then caught the bus again and continued on to Matsumoto, where I spent the night. The next day I explored Matsumoto Castle and the city a bit, and then headed for Tokyo. Depending upon how much hiking you want to do there, you may be budgeting a bit more time than you'll need there. What I did instead of spending multiple days in Kamikochi was to visit Kanazawa and the famous park there, before heading to Takayama/Hida. It was a very interesting contrast IMO between the beautifully manicured and designed gardens/park in Kanazawa and the wild, untouched beauty of the Alps 2 days later.
Finally, if possible, I'd recommend taking one of the days in Tokyo to head north a little ways and visit Nikko. It has a highly ornate and impressive temple complex that is the home of the "See no evil, hear no evil, speak no evil monkeys", and other sites as well. Well worth a visit, somewhat different style than many other temples in Japan.