In Beppu not only the Onsen and the Jigoku Meguri are worth a look. I had the best weather imaginable when I was visiting and I enjoyed walking beside the beach and sitting there, staring out onto the ocean for a long time. It felt so calm and just happy to sit there, enjoy the sun, the wind and the sound of the waves crushing onto the shore.
You could even get yourself burried in hot sand right next to the ocean, unfortunately my time was too short; meaning: I was too chicken to try it. Though I did get the chance later in another place and it really is a strangely great feeling to get burried in the sand. Which made me regret not trying it there even more, but is just another reason to come back one day and lie down next to the ocean and enjoy the sun and sand.
I lost my heart in Japan 