The 14-day Pass should work out just about right. Get a Suica or Pasmo card for travel around Tokyo.

I agree with the above that there is really little need to move hotels between Kyoto and Osaka (and Nara, for that matter.) With a Rail Pass, Kyoto to Osaka is less than a half hour. Osaka to Nara is 48 minutes and Kyoto to Nara is 44 minutes, all on JR lines which you can ride using the Pass. I'd recommend just basing yourself in either Kyoto or Osaka and daytripping among the three and perhaps to Himeji. What time frame is your trip? Himeji Castle is still open but will be under repair starting in the spring.

Unless you will be departing for home from FUK, I'd suggest reversing the order of your visits to Hiroshima and Fukuoka/Hakata and work your way back east toward your departure city from Fukuoka to Hiroshima.

It sounds like you haven't locked your air itinerary yet. Is it possible for you to depart for home from Kansai International (KIX) outside of Osaka? Or perhaps Nagoya (NGO)? If so, and assuming an afternoon departure flight, you could leave directly from Hiroshima to KIX in under 3 hours, saving another hotel move just to get near the airport. From Fukuoka (actually Hakata) to KIX is more like 4 hours. On the other hand, Hiroshima to NRT is over 6 hours.

The only destinations I might suggest fooling with might be to consider cutting a day out of Kyoto/Osaka/Nara and adding it to Fukuoka to allow a visit to Nagasaki or Kumamoto. YMMV.