JR KYUSHU RAIL PASS
JR Kyushu has a great value pass, "KYUSHU RAIL PASS".
They have 2 types of PASS, 1 for 3 days cost 13,000 yen, another one is for 5 days cost 16,000 yen.
You don't need to apply for that from overseas like as JR pass.
It means that you don't need JR pass travelling for Kyushu, You could use your JR pass, may be 7 days in Honshu, tokyo, yokohama, kyoto, osaka, kobe, hiroshima.
JR KYUSHU website
There is a ferry from Hakata international port to Busan, Korea.
It takes just 3 hours, and also they have ferry and Korea rail pass cost about 28,000 yen for 5 days.
This pass include return ferry ticket between Hakata and Busan, and Korea rail pass for 5 days. for more details see the website.