It's a long way from Tokyo to Yamaguchi, even on shinkansen. You can often get good deals on flights from Haneda to Yamaguchi Ube Airport in Ube city, although access is a little inconvenient. There are also direct flights from Incheon in Seoul, South Korea.
The main shinkansen lines linking eastern and western Japan run right through Yamaguchi, making access a breeze, especially if you have a JR Pass.
The slower, more scenic San-in line hugs the coast from Shimonoseki, heading north through Shimane and Tottori prefectures before dropping back down towards Kyoto.