Hakone Area / Mixed Onsen?

Seems like I am too overwhelmed by everything and not able to find an Onsen/Outdoorbath for mixed Genders.

We (M+F) were looking for a Ryokan or Hotel with Private outdoor Onsen but they were out of our budger, so we were searching for public mixed onsen. Unfortunately I can not find any outdoor Onsen/Baths with mixed genders, everything I found was Split Genders, since we want to enjoy the bath and view together we would like a shared onsen/bath.

Has anyone a recommendation for a Bath with mixed Genders and a great outdoor view?
thank you!

by Proof_Buy_6034