By far the easiest way to travel to western Honshu and along its southern shore is by Shinkansen from Tokyo, Kyoto, and Osaka. Major bullet train stops are Okayama, Hiroshima, and Shin-Yamaguchi. It takes approximately four hours to travel to Hiroshima from Tokyo, and less than half that from Osaka.
JR express trains run along the San-yo and San-in coasts, making a loop beginning and ending in Kyoto. Crossing from one coast to the other in western Honshu requires traveling fairly slowly through the mountains.
Local trains and buses run between major towns on the San-in coast, but still nowhere near as often or as quickly as in San-yo. It is always advisable to reserve seats on the popular routes between big cities and to holiday destinations during peak season. Most stations now have tourist offices with English speakers that can help with this.