After visiting Hakatayu we tried to go to Motoyu. Unfortunately — and despite the fact that we got there before closing time — the grumpy old lady who runs the onsen would not let us in. We had already been to Motoyu in March, but then they had changed their opening times and we arrived at a closed door.
My wife was busy, but I decided to give Motoyu one more chance a few days later. This time the owner was much friendlier and I could finally bathe. It's a tiny bath and the water is very hot. You don't get any amenities. I don't remember the price, but it wasn't cheap. Unless you want to get stamps for Kyūshū Onsendō, it's probably not worth it to go there.
Outside Beppu Average price Kyūshū Onsendō Fukuoka-ken