William When it comes to sports, Kumamoto is the perennial runner-up: SO close, but do you remember? (It took our most famous athlete, Shizo Kanekure, 54 years, 8 months, 6 days, 5 hours, 32 minutes, and 20 seconds to complete his marathon.) And who was victorious when Satsuma and Edo trampled? - actually, we didn’t care: it was planting season. The whole “The Last Samurai” stuff happened HERE (look up Tabaruzaka: https://tinyurl.com/ycxb7uvu). We didn’t even get a credit.
But one thing we do have is Fujisakidai Baseball Stadium. Built on what was Kato Shrine until things got all nationalistic and the shrine was moved closer to the castle, the stadium has (in my opinion) the best ambience of any in the world: It retains its 300-year old camphor trees (apparently, Kato Kiyomasa was fond of them as their leaves provided food for horses and their wood fuel - this is why Kumamoto Castle is known as the camphor castle - 銀杏城（ぎんなんじょ).
Even if you abhor baseball (as I do) and have no interest in high school sports (as I don’t), you might want to drop by for a game, if not just for the history. Admire the camphor trees so carefully let be around the perimeter.
Update: Our friend Michael Rupp has noted that camphor are kusunoki (the Totoro tree) and ginkgo biloba are ginnan (the ones that turn yellow on Gakuen Dai and at the Kencho).