
Quick answer
Yamamizuki is the Kurokawa inn most consistently named for its rotenburo — riverside open-air baths set in forest a short drive upstream of the village lanes — a member inn on the nyūtō tegata bath-hopping circuit. Its "best rotenburo in Kurokawa" standing is a consensus of Japanese and English coverage, not an official ranking.
A fuller guide to this inn — its baths, rooms and how to book — is in preparation and will follow.