Hi,
Well, some questions arise from what you write, and many days look very slow and languid. Plus you appear to be doing 6 days of travel on a 5 day JR Kyushu Pass, unless on your Day 6 you plan to go from Beppu to Hakata. If not, you could pay the regular fare from Hakata to Nagasaki (4500 yen) and start using the Pass from Nagasaki.
Also its not clear on your interests - so it's hard to make some suggestions. You name some off-the-trail places like Tochoji and the Nagasaki Aquarium - good to see but most don't put those on their itineraries. How much research on what you want to see have you done?
Anyway, some observations:
For Day 1, most hotels don't allow morning check-ins. Some will keep your bags for you though - but did you confirm this with your hotel?
Tochoji is an excellent and nearly unknown place in Fukuoka. You can get a look of it at:
http://youtu.be/hug3tCMvu28But then you want to see the Tenjin Chikagai, which is almost totally made of women's clothing stores. You can see it at:
http://youtu.be/yQFqmNDTNccIf you want to buy a new skirt or cute pair of heels, you found a good place. Or try the Tenjin Core Bldg. next to the Chikagai at
http://youtu.be/ujaTbf99uEE Otherwise, the Chikagai is usually a way to get from one part of Tenjin to another out of the summer sun, winter cold, or red stoplights.
Plus there are a lot more interesting place to see. Have a look at:
http://www.tinyurl.com/see-fukuokafor lots of good ideas.
Nagasaki is a gem of a city - you list a few good places to go, but if you can, by all means go see Mt. Inasa at night for the spectacular mountaintop night view. Also a frequently missed beautiful temple is Koshibyo, not far from Glover Garden.
http://youtu.be/Mu_JnkVInTUhttp://youtu.be/QdWRyHGW3rkHashima is a great choice also but remember it'll take up about 3 hours and there are only a few ferries leaving per day. See:
http://www.ngs-kenkanren.com/eng/http://www.at-nagasaki.jp/foreign/english/for lots of ideas.
Be sure to try the chanpon and saraudon for lunch or dinner.
Kumamoto is famous for its castle, but don't miss the beautiful Suizenji garden as well; it is one of Japan's finest:
http://youtu.be/K9xyXmU8U1ghttp://www.visitkumamoto.com Mt. Aso is nice too but hard to get to and no guarantee of seeing the volcanic crater if the poison gases are too strong that day.
Kagoshima has its elephant in the room, Sakurajima, but also Senganen Garden, and Shiroyama Park:
http://www.kagoshima-kankou.com/for/http://youtu.be/LxDmLuq6ssIhttp://youtu.be/lpnDK_Wux9QBeppu is really a must-see place as well, for its hot springs, Hells Tour, monkey park & aquarium, plus Mt. Tsurumi mountaintop view:
http://www.city.beppu.oita.jp/02kankou/english/01info/02shisetsu/index...
http://youtu.be/K2NNi8MLcXMhttp://youtu.be/zepPfkuqhokhttp://youtu.be/cBnZneDsKqQ Your last 2 days are pretty vacant - especially day 8 - you can see Canal City in a couple hours; 3 at the most if you really want to dive into shopping. The above link can give you more ideas.