Fly out on the 8th 9th-16th Kyoto 16th-18th Miyajima 18th-22nd - Hiroshima 22nd-29th Osaka, with day trips to Himeji, Kobe, Nara, Mount Koyo, sandakyo Gorge.
Don't know of you've thought about it Paul but a pocket WiFi comes in very handy out there, I used econnectjapan.com last time (and will be again) you could get it delivered to the airport/post office or your hotel.