I hit Kumamoto, Nagasaki, Beppu, Kagoshima, and Fukuoka in five days 12 years back- so keep in mind that my info is old. My interests intersect yours with History, and Experiences/sights. I really enjoyed reading up on Saigo Takamori as most of his story happens in Kyushu and he is a historical hero in Japan. Here were the highlights for me:

Kumamoto: Restored castle, park replicating the Tokkaido road, Musashi Museum (all in Japanese)

Nagasaki: Would spend 2 days minimum- Best A-Bomb museum & cool peace park, Dejima re-creation (major historic significance), great views up the ropeway, great city to walk around. Really regretted keeping my visit to one day.

Beppu: Did the touristy seven hells tour- not necessary but fun. Did the old hot sand onsen as well.

Kagoshima: Sakurajima (not good to do on foot back then), circular bus with lots of great historical sights re: Saigo Takamori.

Fukuoka: Hakata Folk Museum was great, visited the temple where supposedly green tea was first brought from China (wasn't that impressive beyond historical context). Probably could have done something better here.

Nagasaki is great. I recommend three days and spending a half day on the tour to Gunkanjima Island with Gunkanjima Concierge company. Other companies do the tours but Gunkanjima Concierge gives you an English audio headset. Also, I was booked with another company that prematurely canceled two days of trips due to bad weather forecast, Gunkanjima Concierge only canceled the first day and I joined their tour on the second day.

I stayed at the JR Kyushu hotel in Nagasaki connected to the train station, very convenient.

I'll just tell you our plan later this year. Staying 2.5 days / 3 nights in Nagasaki. Get to Nagasaki 1~2pm the first day, few hours to take the family through a tour of the city (29 Martyrs real quick, then tram to Glover Garden, walk back through Dutch slope area down to Chinatown and over to Shianbashi/Kankoudori area). One full day for Haus ten Bos, another full day for Shimabara/Unzen. Not my first time doing any of this. But renting a car for the first time, for at least the Shimabara part. Not used to driving in Jpn, so I'm nervous about that. Thinking about squeezing in Nagasaki Biodome on the same day as Haus den Bos... that would then also require a car, and that might be too much in one day.

Does this tour let you on the island? This isn't something I would do as I'm just not at all into historical tours and such, but I know this is a big thing for many visitors and I'm really impressed that so many foreign visitors take such interest in Japanese history.

Yes, assuming the seas are not too rough, you get off on the island for about 45 minutes. It's also a nice cruise around the harbor even if you can't land on the island.

You might want to think about the Goto Islands also. Way off the beaten path but very beautiful.