14 Day JR Pass

Hello there,

Nice itinerary, I like the idea of traveling down from Tokyo to Fukoaka and flying out from there will save a lot of travel time.

At the same time, this does mean that a 14 day JR Pass would not help you make savings and it is better to buy normal tickets as you travel.

Be sure to drop by Miyajima while you are in Hiroshima.

Hope this helps,
Daniel

A 14 day pass would not pay off with this itinerary. However, if you added a few side trips, you could make it worth it. Spending 6D/5N in Tokyo is plenty and if you added a day trip for example to Nikko it would be helpful and worthwhile. Kamakura also makes a nice day trip. Likewise if you took a day trip to Himeji from Kyoto to see the castle and gardens it would also add value and give more variety.
You can't use the JR Pass near Fuji and Koyasan. For Fuji, visiting Hakone is worth it since if the weather is bad (and it often is) then there are other things to see and do there. Look into these passes:

http://www.japan-guide.com/e/e5200.html

http://www.japan-guide.com/e/e2358_008.html

http://www.japan-guide.com/e/e4900.html

http://www.japan-guide.com/e/e2358_012.html

For Hiroshima don't miss Miyajima as well. Within the city, Mitakidera is a nice temple on the city's west side with nice hillside trails and few venture to see. You also might want to go beyond Miyajima a bit to see Iwakuni with its iconic bridge and mountainside castle:

https://www.youtube.com/watch?v=0COOZXi66mM

For Fukuoka, don't miss the Nanzoin Temple - a secret jewel that few even know about:

https://www.youtube.com/watch?v=lT4VQFmHFyM

http://www.thejapanfaq.com/fukpic.html

https://www.youtube.com/playlist?list=PL7LcPcmoSg-j4RLa6iC7ayvBAbOn8-028

Please be aware that given the length of your trip you can't activate a 14 day pass from your first day in Japan.