We have just had a nice experience in Wakayama and Hyogo prefectures.
We enjoyed Koyasan, where we stayed at Eko-in (thanks to the suggestion of RichardinSF). We enjoyed it but one night was enough for both Ekoin and Koyasan and two would have been too much. I thought the vegetarian food was well flavored but can see how Richard might disagree.
We even more greatly enjoyed Sanso Amanosato, which I believe was recommended by KI-NRT in post number 1 in this thread. The service and attention to detail were of a very high standard. Excellent Japanese-French fusion cuisine. My only suggestion is that the microfiber towels are not sufficiently water absorbent and need to be replaced with cotton. We enjoyed exploring the entire area and found the Niutsuhime-jinja near the sanso to be particularly charming. We also had a tour of a sake brewery associated with Koyasan (self-arranged). The onsen facilities were nice and not too crowded — possibly this was because we came midweek and there were at most 5 occupied rooms competing for the three onsen.
Finally we visited Arimaonsen where we stayed at Taketoritei Maruyama, thanks to KI-NRT’s suggestions. The silver water was really great and was of the rare radium type. The gold water was pretty good too. This ryokan has a number of rental baths with both types so you can go back and forth. We also had a really nice silver water onsen bath in our room. The service here was very good.