While technically not in Beppu, this sightseeing spot can be found right on the ocean along the major road connecting Beppu and Oita City.
Takasakiyama Monkey Park is a monkey reserve found at the base of Mt. Takasaki that is home to around 1500 Japanese macaques. Unlike a regular zoo, this park is notable in that none of the monkeys are kept in cages.
The monkeys you can find at the park are all wild, and freely roam the local mountain, where you can watch them being fed by the employees while enjoying the beautiful view of the bay. Once you’re finished here, you can explore the beachside park that stretches out along Route 10 towards Oita City. * You even can get a combined ticket which includes the return bus trip to and from the aquarium and nature reserve, as well as entry for both attractions! (it can be bought at Beppu train station's information desk and possibly also at Wander Compass).