Your Shikoku excursion will begin and end with trips over the water, and the best way to come or go from Western Honshu is the Shimanami Kaido : ten long bridges create an unbroken thoroughfare between Imabari (just north of Matsuyama) and Onomichi (just east of Hiroshima), across islands in the Seto Nai-kai, Japan's inland sea. Most of these places were totally inaccessible before the bridges were completed in 1999, so the scenery is unspoiled and serene: fishing villages, kaki orchards, seaweed pastures, pearl farms, and a stretch of sparkling sea. Driving, busing, and ferrying from Imabari to Hiroshima are all delightful, and going across with a rental bike is unforgettable.
Biking the Shimanami Kaido is a safe, exciting experience that anyone with a reasonable level of fitness can accomplish. The bridges were built with cyclists in mind: a separate cycling track runs along each one, so you won't deal with car traffic for almost the entire ride. The bridges are flat, and the cycling isn't strenuous. Don't get discouraged by the big corkscrew pathways up from Imabari to the Kurushima Ohashi, or the unattractive hills on the first island, Oshima. After that it's clear sailing.
Biking straight to Onomichi takes about six hours, but you don't have to cycle the whole way: leave the bikes on any of the islands' rental stations and ferry the rest of the way across. Your hotel can send your luggage ahead, so it is the perfect way to travel. For renting bikes, try Imabari's