About 25km inland from Beppu, delightful Yufuin (由布院) sits in a ring of mountains, with the twin peaks of Yufu-dake especially notable. The town thrives on tourism and is a good place to see contemporary Japanese crafts, including ceramics, clothing and woodworking, and interesting foods.
Fair warning: Yufuin has become increasingly crowded in the last several years, especially on holidays and at weekends. You can mitigate the crowds with an overnight stay. Once the day trippers leave, the town reverts to its comfy, intimate self.