We have only visited one onsen in the Horita area, and it was a small charter-only onsen up on a hill looking down over Beppu, called Shiraito no Taki onsen. The onsen is so named for a waterfall cascading down a nearby rock face, which you can admire from one of the baths (or look out over Beppu town from the other 2). With only 3 baths, you need to be lucky with timing, but at only 1000yen for 1hour, this is probably the best value charter bath I have ever been in. The baths themselves are made out of single huge granite rocks, excavated and then carved to make tubs that can fit 2 quite comfortably.
The downside is that there is some material (floating) in the water, which we assumed to be natrually occuring sulfur or similar that is pumped into the baths, not left behind by a previous occupant. There was no sulfur smell or any other sign of dirt; everything looked well maintained and the place only opened in about 2007.
The baths were extremely hot when we arrived, but we were warned about this by the host and showed how to easily turn on and off the cold water tap as we required.
To find this place you will need a car -- turn next to the main Horita Onsen (as though to enter it), but keep going past the complex further up the hill. When you see a waterfall on your left, this tiny onsen is on your right, and looks just like a house with driveway for 2 cars. Definitely worth the adventure, especially for families or couples.
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