Shimanami Kaido is an expressway with a dedicated bike path that connects Onomichi (in Honshu) and Imabari (in Shikoku). You can rent bikes and helmets at one end and return them at the other. The route offers incredible ocean views as it passes over nine islands. You can complete this 60km (~37 miles) ride in a day, but it's worth it to break it up into 2 days and stay overnight on one of the islands.
More info: http://www.jnto.go.jp/eng/location/regional/