Hi Benibu!
I understand! All those places are amazing and all worth a visit. Still you have to make a choice.
Here's what I would visit (based on personal preference):
Day 1 Arrival and travel to Kyoto ,
Day 2 Kyoto!
Day 3 Nara (3 day trip from Kyoto),
Day 4,5 Hiroshima / Miyayima, Start using the 14 day JR Pass (day 4 travel to Hiroshima and local sightseeing, day 5 Miyajima and more local sightseeing, Hiroshima is pretty amazing)
Day 6, Travel to Beppu enjoy a nights stay and visit an Onsen or two (the local sandbath's are very nice too)
Day 7, more Beppy and after noon train to Matsue
Day 8 Matsue, sightseeing (my personal recommendation is to see the Adachi Museum of Art
Day 9 Travel and stay in Tottori
Day 10, Daniel's san special visit to Kinosaki Onsen a very lovely onsen town best visited for a single nights stay.
Day 11. On to Kanazawa, it's a long ride (about 5 hours) but absolutely love Kanazawa. The city is very beautiful and less frequented by foreign visitors giving it a unique Japanese atmosphere. The Castle and castle park are beautiful as well as the Kenroku-en Garden.
Day 12. Kanazawa - After so much travel I think that you deserve an other day to relax and explore the city. There's an old Geisha District which was never touched by the 2nd WW and retains it's original beauty. You could also make a day trip by bus to Shirakawago which is a beautiful traditional village.
Day 13. Time to head slowly to word Tokyo - but first a nights stop at Takayama
Day 14. Enjoy a little more from Takayama before heading to Tokyo. It's quite a ride to Tokyo so be sure to bring a good book.
Day 15. Day trip to Nikko! Nikko is amazing and making a day trip with your JR Pass there, really is making the most of your Pass, return to Tokyo by evening.
Day 16. Tokyo and last day shopping!
Day 17. Fly back home - last day of JR Pass - that was one amazing trip!
Well, that's how I would do it. You would see a lot, visit 2 Onsen places (Beppu and Kinosaki) see some of the most beautiful towns / cities of Japan (Kyoto / Kanazawa and Takayama) and really make the most of your JR Pass (I would not be surprised if you made 100% in savings of the original price).
Let me know what you think!
-Daniel