The new IC Beppu has many rooms with in-room onsens on the balcony and an absolutely beautiful public onsen facility. Also very closely located to other onsens worth a day trip in the Oita/Beppu area (some just minutes away from the IC Beppu). 2 hours from Fukuoka/Hakata on the JR Kyushu Limited Express Sonic train.
Photos from my stay in November:
-FlyerBeek