Tenzan Tōjigō is one of Hakone's better-known day-use onsen, tucked in the hills above Hakone-Yumoto. It is built around outdoor baths, timber, stone, and steam rather than hotel polish, which makes it a satisfying stop even if you are not staying overnight in a ryokan.
The baths are segregated by gender and follow normal Japanese bathing etiquette. Go outside peak weekend hours if you want the calm version of the experience; Hakone is popular enough that famous bathhouses can fill quickly.