As far as getting to Nikko and back, you should look into the Nikko Passes. I used
the world Heritage pass, which does not seem to be available right now.
The two day Nikko pass allows you to go up one day, stay in an Onsen, and then go back to Tokyo the following day. These use the Tobu private train lines, which are not covered by a JR Pass. When I went, I stayed in Kinugawa. Here is the link showing all of the flavors of Nikko Passes:
http://www.japan-guide.com/e/e2358_002.htmlThis takes care of the Tokyo to Nikko Part.
If you go to the Nohi Bus website that I gave you, you can get information about the Tokyo to Takayama bus, and the Takayama to Kyoto bus, including the price. The costs are 6690 and 4200 yen, which comes to 10890 yen for both. This is less than the 13000 yen, which is the difference between the 14 and 21 JR Pass.
The thing is, you have Koyasan, Naoshima, Hiroshima, and the Hakone area left, and you plan to do those in seven days. You may only need a 7 day pass. In this case, you may be looking at about the difference between a 7 day, and a 21 day pass, which is more like 30,000 yen.
By the way, getting to Koyasan is through a world heritage pass that uses the Nankai private rail system, so that also will not be covered by the Jr Pass.
http://www.japan-guide.com/e/e2358_012.htmlGetting around Hakone and mount Fuji are is also not covered by the Jr Pass, and you will probably be getting some flavor of Hakone or Fuji Passes. More links:
http://www.japan-guide.com/e/e2358_008.htmlhttp://www.japan-guide.com/e/e2358_014.htmlhttp://www.japan-guide.com/e/e6905.htmlSome of these passes will get you back to Tokyo, so the Jr pass only needs to get you from Hiroshima to Odawawa, which is the station where the Hakone or Fuji-Hakone passes start.
Your 7 day JR Pass would be effective to do the following:
(1) Last day in Kyoto: Day trip to Nara.
(2) Travel to Osaka: To go to Koyasan.
(3) Travel to Okayama: to go to Naoshima
(4) Travel to Hiroshima
(5) Day trip to Miyajima Island
(6) ???? Open Day ?????
(7) Travel to Odawara: to go to Hakone.
If you do not know what to do with the open day, I would suggest using it to reposition from Koyasan to somewhere near Okayama, and then do Naoshima Island as a day trip. Kurashiki is nearby, and would work:
http://www.japan-guide.com/e/e5750.htmlThis would make this part of the trip look like this:
(1) Last day in Kyoto: Day trip to Nara.
(2) Travel to Osaka: To go to Koyasan.
(3) Travel to Kurashiki
(4) Day trip to Naoshima
(5) Travel to Hiroshima
(6) Day trip to Miyajima Island
(7) Travel to Odawara: to go to Hakone.
Here is information on travel to Naoshima Island:
http://www.japan-guide.com/e/e5476.html?aFROM=5475_5700This is just a suggestion. What you may start to understand is that the JR Pass is great for distance travel, if you can clump it together, but local travel is sometimes best by other transportation.
I hope this helps.