You could visit Miyajima - it's free to take the ferry over there if you have a valid JR Pass. Miyajima is a small, silent and peaceful island with a very famous shrine in the water just before you reach the island. There isn't much to see/do there apart from the island itself (and its nature) but I spent 5-6 hours there last year and I don't regret. There are some walking routes on some quite steep mountains, beautiful view of the sea and a few small rivers and you will probably meet some deer’s as well. It's quite easy to get there by train from Hiroshima. Not many shops in the area apart from small souvenir shops and a 7/11, so you may wish to bring some food with you if you plan to stay there for a while.
See:
Miyajima Travel Guide