Help with Itinerary

Hi,
We plan to spend 2 weeks in Japan, flying in and out of Kansai airport.
Here's our tentative intinerary:
7 nights Kyoto (renting an apartment, 7 nights minimum stay) including day visits to Osaka
Hiroshima/Miyajima
Takayama
Mt Koya (overnight)
Hemeji

I have the following questions?
1. In what order should we arrange to visit the cities beyond Kyoto without doubling back?
2. Should we get a 7 or 14 day rail pass?
3. Any other suggestions for places to visit?

Thanks for your help and suggestions.

Osaka local commuter train, Hiroshima by hikari shinkansen, Takayama 4 hours by Ltd Express so overnightstay in Takayama recommended. Himeji by shinkansen, Mt Koya private railway. If Osaka, Hiroshima, Takayama and Himeji within 7 days then 7 day JR Pass. Doubling: The Hikari shinkansen goes: Kyoto - ShinOsaka - Himeji - Hiroshima. Takayama and Mt Koya different areas.

An overnight stay is strongly recommended for visiting Takayama.

And I also recommend and overnight stay for visiting Hiroshima and Miyajima, unless you do not mind traveling at a very fast pace.

Thank you for your suggestions. Upon during more research, my tentative plans are as follows:
7 days Kyoto with day trips to Himeji, Osaka
Day 8: Kyoto to Hiroshima, overnight Hiroshima
Day 9: Hiroshima to Miyajima, overnight Miyajima
Day 10: Miyajima to Kanagawa, overnight Kanagawa
Day 11: Kanagawa
Day 12: Kanagawa to Takayama, overnight Takayama
Day 13: Takayama to Osaka
Day 14: Osaka to Kansai

1) Should we overnight 2 nights in Kanagawa or 2 nights Takayama?
2) With this itinerary, I think I could buy a JR West Kansai Rail Pass for the first week and a 7 day JR pass for the second week.
Any thoughts?

Is it Kanagawa or Kanazawa?

Sorry, it should be Kanazawa.

Your leg from Miyajima to Kanazawa will be a long one, almost 6 hours with 2 transfers. I suggest you spend two nights in Kana then take the bus to Taka and spend one night there.

For a unique experience, you should also consider staying at Koyasan and Shirakawago. Both places offer you something that the big cities do not. They were the highlight of my trips to Japan.