Joe Tomei here, hearing that a few folks are coming to Kumamoto from April, so this is a thread for suggestions and information. Here's a few things, if I'm wrong, please let me know and I'll edit and if you have anything to add, drop it in the comments and I'll move it up here.
-I think a lot of official services (juminhyo, koseki) are available online IF you have your My Number card
-almost everything is handled at the various ward offices
https://www.kurunavi.jp/en/municipality/43.html
-visas are handled at the Dai 2 Godochosha (map in Japanese here http://houmukyoku.moj.go.jp/kumamoto/table/shikyokutou/all/honkyokutouki.html)
-public transport in Kumamoto city is a bit complicated, though they are merging the 5(!) public transport companies in April because of the decline in passengers due to corona
https://www.sankei.com/region/news/200128/rgn2001280022-n1.html

Any other useful hints? Drop them in the comments!