Sanyo San'in Northern Kyushu Pass 

Here is a pass that will allow you to travel in western Japan via Nara, Osaka, Kyoto to Fukuoka on the island of Kyushu .

With this PASS it is possible to travel throughout the west of Japan (even by Hello Kitty Shinkensen!) up to the north of Kyushu. The ferry to Miyajima is also included in the PASS

Per adult, it is 142€ for the week which could be   much more cost-effective than taking each train independently. Just Osaka-Fukuoka costs €100! It all depends of course on where you want to go.