Hiroshima and Miyajima are about an hour from each other, so if one of them is in your itinererary, the other should be too. If you have the JR Pass, it costs you nothing additional to travel between them. Half a day is about enough to cover the main sights in Hiroshima and Miyajima, i.e. the Atomic Bomb Dome in Hiroshima and the Itsukushima Shrine with its great Torii gate, in Miyajima. These are UNESCO heritage sights.
The Atomic Bomb Dome as viewed from the monument in the Memorial Park.
I read about recommendations (from tabelog.com) on the restaurant specializing in eels in Miyajima – うえの. This restaurant is very near the train station. In order to satisfy my craving for both the oyster and the eel, i bought the eel bento (which was not cheap, at more than 1700 yen). The bento was fantastic. The eel was like nothing i have tasted before. The textue is not the typical mushy type, and the taste was not the typical “drowned in teriyaki sauce” kind. If you want to taste eel like you have never before, go here. At least grab the bento.