Kurokawa's popularity has been increasing so prices have shot up especially in the luxury segment and English speakers. There are a few onsen towns near Kurokawa which are less expensive and still mostly domestic travelers. There's a good kurokawa onsen hopping blog by a English teacher who teaches ryokan staff
https://kurokawa-onsen.com/category/onsen-hops/ Onsen hopping with an onsen pass is one of the selling points in Kurokawa. I stayed at two high end ryokans around Kurokawa last fall, one a repeat, as part of a special occasion trip. Kurokawa is a few hours from Oita or Kumamoto by car or bus so while you could make it for a 2 night stay from ITM/KIX or HND, you might lose a few hours of onsen time to transit.
The Kurokawa thread also mentions a few other towns (a map feature would be helpful) I'd probably head for Hirayu or Fukushima if the weather lines up rather than Northern Kyushu for 2 days. I'd allocate more than 2 nights for Kyushu or Hokkaido onsens since there is a lot of quality water.
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Hot springs along the new Hokuriku Shinkansen route to Kanazawa?