What to see depends a lot on your interests of course, but whatever it is, Kyushu has a lot to satisfy nearly any traveler.
The above link to the old thread is also of limited use since it deals a lot with driving, and was made before the bullet train linking from north to south was completed.
If you really want to take the full 9 days, the a 2 week full JR Pass would be cost effective. You could take a bullet train from Osaka to Kagoshima and start touring, then end up in Hakata or Kokura and take the bullet train back to Osaka (or vice-versa). But if you're willing to cut your time down to a 7 day trip in Kyushu, you could get a 7 day rail pass and that'd be a better value.
There is a ton of good places to see.
For 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 wooden Great Buddha:
https://www.youtube.com/watch?v=hug3tCMvu28Dazaifu is also famous for its large Tenmangu shrine:
https://www.youtube.com/watch?v=BwxGPZxPlNwIn 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_JnkVInTUSaga is mostly mountains, and famous for Arita pottery, Takeo onsen, and Karatsu seaside castle. If you're not into porcelain than you can skip it.
Oita has some nice sites too. Beppu is famous for its hot springs, Hells Tour, plus monkey park & aquarium. See:
http://www.city.beppu.oita.jp/02kankou/english/01info/02shisetsu/index...https://www.youtube.com/watch?v=K2NNi8MLcXMhttps://www.youtube.com/watch?v=zepPfkuqhokhttps://www.youtube.com/watch?v=cBnZneDsKqQKumamoto 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.
Kagoshima is great to see the live Sakurajima volcano, hiking, and hot sand baths such as on Ibusuki. Plus the Senganen garden has a superb backdrop view of the bay and the volcano. See:
http://www.kagoshima-kankou.com/for/https://www.youtube.com/watch?v=LxDmLuq6ssIhttps://www.youtube.com/watch?v=lpnDK_Wux9QPlus Miyazaki has some very pleasant beaches, and its Takachiho Gorge is remarkable (but you can't get there by rail).
http://www.miyazaki-city.tourism.or.jp/en/ http://www.kanko-miyazaki.jp/english/ https://www.youtube.com/watch?v=H49x41ViFJkLastly if you have time, Kitakyushu has a few sights of interest also. It's Kokura Castle is one of the better ones, the view from its Moji wharf and preserved buildings are quite historical, and the view from atop Sarakurayama is one of Japan's best and rarely mentioned:
https://www.youtube.com/watch?v=Hl1pCW9IbbkFor comprehensive info on Kyushu, see:
http://www.visitkyushu.orgEnjoy your trip!
