The mountainous island of Ōmi-shima (大三島) is connected by bridge to Ikuchi-jima to the east and Ō-shima to the southeast. It is home to one of the oldest Shintō shrines in western Japan, Ōyamazumi-jinja, near Miyaura port. The deity enshrined here is the brother of Amaterasu, the sun goddess. The present structure dates from 1378, but in the courtyard is a 2600-year-old camphor tree, and the treasure hall contains the most important collection of ancient weapons found anywhere in Japan.
It's worth getting off the 'recommended' cycling route to explore Ōmi-shima. With more time on the island, don't miss the Tokoro Museum, a small but interesting collection of modern sculpture. It's a hilly ride up to the museum, but you're rewarded with fabulous sea views.