Onsen ryokan stays in Japan are normally short, usually one or two nights. But, if you're on vacation and visiting from abroad, I think 3-4 nights would be the maximum I would want to stay there, for me, 3 nights would be enough. We had a car when we stayed but did almost no sightseeing while there as we were traveling with my wife's elderly mother. There is not a lot to see or do near the hotel. Here is a link to the IC Beppu's activities page of their website with things to do in the area. https://www.ihg.com/intercontinental...tail/concierge

I've only lived in Kyushu for 5 years, so I still have lots of exploring to do. Living in western Kyushu, I haven't seen that much of eastern Kyushu (where Beppu is), but if you plan ahead I think you'll find there is plenty to do. If you have time, you could drive down along the east coast down to Miyazaki and to Kagoshima. There is also the popular onsen town of Yufuin, which is inland from Beppu, but not that far. It is much smaller than Beppu.
https://www.japan.travel/en/spot/707/
https://www.japan-guide.com/e/e4750.html

Since you'll have a car, you could also take the car ferry from Beppu to Osaka or from Oita City to Kobe, if you plan on visiting Honshu. They also have a ferry from Kagoshima to Osaka.
https://www.ferry-sunflower.co.jp/en/

I hope Japan opens to overseas visitors in 2022, I think a Q2 opening is fairly likely.