Hi Gary!
I made an itinerary to help you out here! I mainly based it on travel times to gives you as much time possible to explore Japan!
Day one - Arrival
See a little of Osaka, relax from flight, enjoy a Japanese cuisine.
Day two - Travel to Kyoto
Explore Kyoto and sightseeing.
Day three - Kyoto
More sightseeing in Kyoto, perhaps visit Fushimi Inari.
Day four - Travel to Hiroshima - Activate JR Pass.
Hiroshima sightseeing, I would recommend a visit to both the peace museum and memorial park, stay the night in Hiroshima.
Day five - Travel to Tokyo with a stop at Himeji
Early bullet train to Himeji, enjoy the castle and perhaps more sightseeing, after couple of hours back to station and Bullet train to Tokyo. Stay night in Tokyo
Day six and seven
Tokyo, Tokyo and more Tokyo! Visit Asakusa, Ginza, Shibuya. My other recommendations would be Akihabara (Electric Town), Harajuku and Tokyo Tower.
Day eight - Yokohama (and maybe a little Tokyo).
Take a local line or Shinkansen from Tokyo to Yokohama for a good day of sightseeing in Yokohama, be sure to visit China Town here! Evening return to Tokyo for a last night there.
Day 9 - Return to Osaka/Kobe
Your last day in Japan, you can either spend your last night in Osaka or go to Kobe to finish the tour. Both places are on the Shinkansen and not far from each other. I would say go Kobe and make the most of your trip and JR Pass. In Kobe you can visit some of the local attractions like the Sake breweries or enjoy a beautiful view of Kansai from the nearby mountain called Mt Rokko.
Day 10 - Return to Kansai Airport and flight home.
Take an train either from Osaka / Kobe and travel to Kansai airport to catch your flight back home.
This pretty much is how I would do it, let me know what you think!
-Daniel