We did a week of riding/train combo in Kyushu over thanksgiving on bike friday. One of our best vacations!
Day 1 Fukuoka to Hita via Dazaifu temple, stayed in the ryokan with onsen.
Day2 Hita to Usa, via maple cycling road with a stopover in Rakanji Temple - both very highly recommended. Stayed in Naru guest house in Usa.
Day 3 Kunisaki penninsular,
https://www.japan-guide.com/e/e4724.html Fukiji , Futagoji, Usa temples. The highlight of the trip!!! We then rode to Kitsuki and took a train to beppu. If I do ti again I would stay in Kunisaki or somewhere near Oita airport. Too much too see on the penninsula for one day.
Day 4 Beppu to Oita with a visit to couple of hells, sand onsen and Monkey Mountain. We spent so much time in the attreactions that we decided not to ride to Saiki (original plan) and took a train there. Saiki is the place to have sushi. If you have a time - ride to Tsurumisaki Lighthouse, eastmost point in japan - (we did not have time)
Day 5 - train to Kagoshima, rode around there
Day 6 - ferry to Sakurajima, rode around the volcano - highly recommended. train back to Fukuoka
PS. When planning, the area around Aso looked very nice as well. Did not get to go. there is a facebook group on Japan touring with tones of advice.