Not so fast.
First, why would you think you could use a Kyushu pass from Osaka??
At any rate, unless you are leaving for Japan soon, the JR Sanyo-Shikoku-Kyushu Rail Pass will be discontinued on March 31, 2015.
For info on regional Japan passes, see:
http://www.japan-guide.com/e/e2357.htmlFor complete info on the JR Kyushu Pass, see:
http://www.jrkyushu.co.jp/english/railpass/railpass.jspAt least they updated their map which was previously very misleading. At best you can go up to Shimonoseki on the pass. Be aware though that you cannot take the bullet train between Kokura and Hakata - you can only take other trains like the Sonic limited express.
Beppu is a nice city for its hot springs, but also for its Hell Tour and nearby monkey park:
https://www.youtube.com/playlist?list=PL7LcPcmoSg-hOggZamc2lUNTr46ApKX...In terms of history and varied points of interest, Nagasaki is really the most interesting city on the island. It is worth a couple days to see the city, and another day to see areas nearby like Shimabara/Unzen or whatever interests you. Gunkanjima, while it takes 3 hours, will blow your mind.
http://www.ngs-kenkanren.com/eng/http://www.at-nagasaki.jp/foreign/english/http://www.youtube.com/watch?v=QdWRyHGW3rkBe sure to see Mt. Inasa at night if the weather is clear, and try the Nagasaki chanpon and saraudon! Also the Koshibyo temple is an often overlooked shrine that is quite unique in Japan:
https://www.youtube.com/watch?v=Mu_JnkVInTUFor Fukuoka, there are many open parks, shopping, seaside historical areas, and urban neon. See this site as a good guide:
http://www.thejapanfaq.com/fukpic.htmlThere are also many useful videos to give you a preview:
https://www.youtube.com/playlist?list=PL7LcPcmoSg-j4RLa6iC7ayvBAbOn8-0...
Look into a Fukuoka Tourist City Pass also:
http://yokanavi.com/access_tourist_egBe sure to try the tonkotsu ramen at least once, and see the 2 Great Buddhas:
https://www.youtube.com/watch?v=lT4VQFmHFyMhttps://www.youtube.com/watch?v=hug3tCMvu28Kumamoto is famous for its castle, Suizenji Garden (a must-see), Mt. Aso and Kurokawa hot springs.
http://www.visitkumamoto.com/http://www.pref.kumamoto.jp/english/pdf/kankou_e.pdfhttps://www.youtube.com/watch?v=K9xyXmU8U1gNote that you can't get to Kurokawa by rail.