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.