If you have time and would like to explore more, there are other passes that might help you too, by the way. You might look at the various passes from JR West.
The Sanyo-San'in Area pass is one of the most far reaching and you can travel a lot, and for less than the regular JR Pass. There is lots to explore and enjoy. Okayama is pretty close and it is famous for its castle, plus Korakuen, one of Japan's Top 3, and also the Handayama Garden. If you'd like to get off the typical tourist path for a while, the half day hike up to Konpirasan in Kotohira is stunning. Going to Takamatsu is also nice - it has one of Japan's nicest gardens also, called Ritsurin.
Hiroshima also has a number of great spots. Miyajima is the most famous, and aside from Hiroshima itself, Onomichi with its temple tour and Kosanji Temple is spectacular. Just beyond Miyajima also lies Iwakuni with its historical bridge and castle on top of the mountain. Taikodani is also a beautiful shrine in Tsuwano, Shimane.
Hagi Castle was actually delightful, and the preserved samurai district and Mori related temples a rarity. One of the very best is the Akiyoshi Limestone Cave, a 300 million year old wonder with huge caverns and underground river running through it.
Even Kyushu is not far if you want to see it. Fukuoka is one of the nicer cities there. There are many open parks, shopping, seaside historical areas, and urban neon. See this site as a good guide.
Don't miss the Nanzoin Temple which is one of Japan's finest yet almost totally unknown to the outside world and completely free.
Look into a Fukuoka Tourist City Pass also.
You can also see a lot of previews on the best there is to see here. You could expand your plans a bit and see Nagasaki as a day trip if you start early - there is a lot there - the best sights are the Peace Park/Museum - but if you see the one on Hiroshima you might skip it - Glover Garden, Dejima, and Koshibyo Shrine. Gunkanjima would also be well worth seeing, but it takes 3 hours. And at night be sure to go see Mt. Inasa at night for a spectacular night view over the city.
Or, see Kumamoto for its castle and wonderful Suizenji Garden. Beppu is another possibility and famous for its hot springs, but its Hells Tour, plus the Takasakiyama monkey park/aquarium are all terrific. The best hot springs though you'd need to take a bus to get to, but Kurokawa in Kumamoto is one of Japan's finest hot spring resort areas with beautiful forested outdoor baths.
Have a great trip.