@MoH Great, then for me, the most interesting aspect of Kyūshū is further south, in Kagoshima (straight south of Kumamoto) and Nagasaki (south west of the Island but across the Ariake sea). That’s where you can catch up on the root of the modernization of Japan, for these two spots double as the entry point to Japan for both the Korean and Chinese neighbors, and more famously Westerners (the Portuguese, then the Vereenigde Oostindische Compagnie, then the British Empire) and their new technologies.
The Nagasaki connection is well known, and Dejima is interesting but visiting it won’t give you that much more than what you’d get from a book or a good video essay on Youtube. The most interesting Western settlement in the city is actually the Glover Garden, a pretty nice garden on one of the hills above the harbor, which has preserved the mansions of the British dignitaries that lived in the premises from the Meiji restoration until WW2. Most of the tour is dedicated to the incredible impact of the Scotsman Thomas Glover, who was instrumental in the modernization of Japan, both for his personal economic interest and to screw with the English. He was involved in the import of railroads, reverberatory furnaces, modern weapons, beer breweries etc. and became the key foreign figure of the early Mitsubishi industrial empire (hence the Mitsubishi factories the US clumsily tried to erase with Fat Man in 1945).
Obviously, the museum and garden dedicated to the second atomic bomb are a recommended (if chilling) visit as well. The local catholic churches were less interesting than I expected – mostly because the only cool one was destroyed by Fat Man – but I do recommend the Suwa shrine which was built precisely to make christianity less fashionable and reconvert locals to Shinto. It’s a pretty fun religious dick contest to digest.
Since you might have a car, the nicest way to drive to Nagasaki might be to go straight and enjoy the ferry trip on the Ariake sea. It will take you slightly longer (about 3 hours) than driving (or taking the three trains necessary to go) around the Ariake sea (about 2h30min) but the experience itself is probably worth the extra 30 minutes.
Kagoshima is less widely known for its historical impact, but it is the home of the Shimadzu clan which is one of the coolest clans in Japan, constantly surviving wars, betrayals and their own bad decisions through the skin of their neck because they were too useful as the only known diplomatic point of contact to Korea, China and many foreign powers. The Shimadzu clan even created the modern Japanese flag hinomaru, because they were the first to build a modern warship, which also begot the first time Japan had to symbolically represent its nation on neutral ground.
If you are interested in this historical perspective, there is a commonly recommended Museum of the Meiji Restoration that’s kinda crap – or at least completely unnecessary because of my two recommendations. The first is the Reimeikan, or “Kagoshima History Museum and Fine Arts Center”, which has an even better and deeper explanation of the Meiji restoration on one of its floors. I stayed at the Reimeikan more than two hours and could have spent twice as much. The second is the personal residence of the Shimadzu family, the Sengan-en, which hosts not only a beautiful Japanese nobility residence where the Emperor and his family went to chill a few times, but also the UNESCO-protected Shoko Shuseikan museum, another great museum on the technological transformations of Meiji Japan, but from the amusingly more biased perspective of the Shimadzu clan. The Sengan-en is a bit far from the city center but perfect opportunity for a quick drive (or 20min taxi ride).
Kagoshima also has its own active volcano to visit, on Sakurajima, famously facing the city. You can reach the Yunohira Observation Deck via a ferry and roughly 20 minutes drive from the dock.
Food recs:
In Nagasaki…
Mutsugoro
Dejima Asa
Maruni Miso Ramen close to Nagasaki station
Hakata Motsunabe Ōyama next door
Bread A Espresso (but go early, sells out quickly)
Kōzanrō (although I think champon is overrated)
The honten of Castella Bunmeidō
In Kagoshima…
Uoshō (wonderful kaisen but nihongo only)
Hangyojin
Yakiniku Kamichiku
Roppakutei (or any kurobuta shabu, really)
Kairaku to try the local clam soup
Wasabi for a useful izakaya downtown
Nomura for exceptional ¥30,000 sushi
Ōkatei at the Sengan-en
The regional fruits section at the Yamakataya department store
Lastly, having your own car is a unique opportunity to go to a remote onsen. I had a wonderful time in a luxury one with an ex-girlfriend, private onsen in the room and everything, but there are myriads of options for all vibes and all budgets in a two hours drive radius if your home base is Kumamoto.
Hakata/Fukuoka is culturally pretty meager compared to these cities. Much more interesting for the people living there (especially the artists) than the city itself. Never been to Beppu, so I might be underestimating that side of the island, but it also feels like a lesser priority to me than Kumamoto, Kagoshima and Nagasaki.