For example if arriving from Hakata, you can take special train 'Yuyfuin no mori'
Yufuin is famous for onsen, many hotels/ryokan have own onsen, and there are also traditional ones allowing day guests for the bath
traditional style streets with craftman works, food, pastry, cake
hiking:
Yufuidake is near and can be hiked, but in January when I was there it was snowing and there was ice - I returned 20min before the summit.
Hidake/飛岳 can also be hiked. According to Osmand (with openstreetmap material) via 2 ways, one from the south and one from the north. At least as of 2022 the one from the south is really bad towards summit, I aborted 15min before summit.
various museums and exhibitions. I liked: Showa museum, Comico art museum