Beppu is very far away, busy and not particularly famous for outdoor baths, although there are a few, including one on the roof of the Suginoi Ryokan with spectacular views (not obstructed by any fence) over the city. It is gender separated and costs 2000 yen for a day-visit. In many ways, probably not the type of bath you are looking for.Takaragawa Onsen is a huge outdoor bath in the mountains of Gunma. Depending on timing, it can be calm or very crowded:
http://www.takaragawa.com/english.html
The Okuhida area in the Japan Alps has some of very spectacular outdoor baths. I especially enjoyed the baths of the Suimeikan, whose main bath, I believe, is gender-mixed:
http://www.nande.com/karukaya/top/index.htm
Kurokawa Onsen on Kyushu has also some spectacular baths. My favorite is the Yamamizugi.
