Khaosan Beppu is more of a guesthouse than your average hotel.
N and I stayed there during our trip to Beppu around 2008. The place is about 8-10 minutes walk from JR Beppu Station, very convenient. It has it’s own Onsen(Spa) which is free, kitchen and free use of the internet. During our stay there were no Wi-Fi yet.
I think N and I booked Basic Twin Private room for the night. The room has a double deck bed, and futon set but N and I decided to sleep in the floor instead since nobody wants to be on the top bed :p, it has tatami floor so no problem.
Convenient, affordable and clean.