In 2018 we stayed at Iyashi no Sato Kiyashiki which is a couple of hours from Fukuoka and loved it. Quite nice rooms, you could book one with an outside bath, food was excellant (the basashi a real standout which is understandable for the location), it had a really nice bar looking out into the scenery which was lit up at night which was great for an after dinner nightcap and the public bath which you could book for private use had a beautiful outlook and was a bit of a highlight of the trip.