Have u been to Ehime Prefecture? You can take the ferry from Hiroshima to Matsuyama , Ehime Prefecture. Dogo Onsen is very nice.
Yamaguchi Prefecture is also very near Hiroshima, I think about 40 minutes from Hiroshima Station. The Kintaikyo is very beautiful.
If you are taking the JR Pass, try going all the way to Beppu.
Since you like the culture, I recommend to visit Usuki Oita. Its an hour a way by train from Beppu Station.
If you like Onsen, try visiting Kinosaki Onsen in Kyoto too.
