Colder in Kyushu than Honshu?
Nonsense.The colours in Kyushu during the fall are some of the most beautiful anywhere. One especially popular place is Akizuki, sometimes referred to as a "Little Kyoto" because of its colours and popularity.
http://www.youtube.com/watch?v=S0-YxwfD340Another spot that is gorgeous but far lesser known is Miyama, with its Kiyomizudera temple (not to be confused with the more famous one in Kyoto).
https://www.youtube.com/watch?v=jKAMjJ4VrToThere is far more to see and do than just look at the trees though. If you like hot springs, you've found the right place. There are many, including Beppu, Yufuin, Kurokawa, Takeo, Unzen and Futsukaichi.
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...Don't miss the Nanzoin Temple which is one of Japan's finest yet almost totally unknown to the outside world and it's *FREE*!
https://www.youtube.com/watch?v=lT4VQFmHFyM Be 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=BwxGPZxPlNwNagasaki is really the most interesting city on the island. It's 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, is stunning.
https://www.youtube.com/playlist?list=PL7LcPcmoSg-gbw2yXNLK92siHyNqSNx...Oita has some nice sites too. Beppu is famous for its hot springs, Hells Tour, plus monkey park & aquarium.
https://www.youtube.com/playlist?list=PL7LcPcmoSg-hOggZamc2lUNTr46ApKX...Kumamoto is famous for its castle, Suizenji Garden (a must-see), Mt. Aso and Kurokawa hot springs.
http://kumanago.jp/en/https://www.youtube.com/watch?v=K9xyXmU8U1gNote that you can't get to Kurokawa by rail, and the area near the Aso crater is currently closed off.
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=H49x41ViFJk