You can see Miyajima easily on a day's trip from Hiroshima, but because it's such a beautiful respite from city life and because most tourists are day-trippers, you'll enjoy the island much more if you stay behind after the last ferry leaves. An added benefit of a longer stay: Itsukushima Shrine is illuminated at night, a gorgeous sight overnighters should not miss. I've therefore included a few recommendations on where to stay, but avoid Golden Week and weekends in July, August, October, and November (when maple leaves are in full color), because accommodations are usually full.
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.