Onsens! Onsens! Onsens! This is certainly what this Prefecture is famous for but there is a lot more offer from ancient Buddhist images to theme parks. With a much more laid back feel compared to the big cities of Honshu this is a good place to dive into the more rural Japan off the beaten track.
The Oita dialect differs a little from basic Japanese but not too much to cause any problems. A good English speaking information centre is located at Beppu Station and is reccomended to plan parts of your trip.
Located approximately 25 miles northeast of Beppu, Oita Airport is the main commercial airport in Oita Prefecture and has daily services to and from Tokyo, Osaka (both Kansai and Itami) and Nagoya by both JAL and ANA as well as a single international flight to Seoul, Korea with Korean Air
Travel between the airport and surrounding cities and towns are handled by bus and hovercraft, unfortunately lacking any train access as of yet. The bus has an approximate travel time of 45 and 60 minutes to Beppu and Oita, respectively. The hovercraft trip is significantly faster, only taking 25 minutes, and deposits passengers at a landing in Oita just east of the Oita River. Access between this landing and the city's downtown takes approximately 10 minutes via taxi or bus and about 1 hour
Three JR Kyushu train lines run through Oita Station, located downtown: Nippo Honsen, Hohi Honsen and Kyudai Honsen. The Nippo Honsen could be considered Oita's main rail access line, running JR Kyushu's Sonic trains from Hakata Station and reaching as far south as Miyazaki. Sonic express trains take approximately two hours to and from Hakata Station. This line also stops at Nakatsu, Usa, Hiji, Beppu, Usuki and Saiki. The Kyudai Honsen has local service running to the west through Yufuin adn Hita and reaching as far as Saga Prefecture. Finally, the Hohi Honsen runs local and express service through Bungo Ono to Kumamoto City, Kumamoto Prefecture.
Buses from virtually every major city on Kyushu have service to Oita and Beppu, the main ones being the multiple highway buses that run to and from Fukuoka. Oita Bus, Oita Kotsu, Kamenoi Bus and a handful of others offer this highway service and travel time is approximately two hours, nearly identical to JR Kyushu's Sonic.
To get to some of the smaller places hiring a car is a very good or only option as public transport can be rare and not particularly convenient. For the cities the train service is the most convenient way to get around. The JR Kyushu Pass is well worth getting and can make travel relatively cheap.
Another option is hoping on a bike! With beautiful scenery, friendly locals and numerous onsens Oita is a great place to bike around. Every March there is the annual Oita Charity Bike Ride that tours around the Ken. Refer to www.oitajets.com for further details.
Stone Buddhas in Bungo Takada- where Buddhism and Shintoism are said to have fused in Japan
Shouen Village in Bungo Takada- where the landscape and rice fields have kept the same natural scenery in tact for 800 years. You can experience a farm stay here
Yufu River Gorge- A ravine formed by Yufu River which flows between the Yufudake and Tsurumidake mountains.
Matama Beach- A beach on the west end of Kunisaki peninsula, which forms tidal flats at sunset to make for the designation of "One of Japan's Best 100 Sunsets"
Harajiri Falls in Bungo Ono- "The Niagra Falls of Japan" and "One of Japan's Top 100 Waterfalls"
Hiking Mount Yufu, or Mount Kuju- which is the highest mountain in Kyushu. The Olle hike called the Okubungo Course is a beautiful hike through the country side of Kyushu, especially in spring (cherry blossom) or autumn (red leaves) The hike can be done from either Asaji or Taketa going either direction. At both villages they start at their respective train stations. Both train stations have a small information office. The hike can be done as a day trip from either Oita or Beppu. The hike brings you along a little tree lined lake, a stone wall Buddha, and an old castle. After the hike you can relax in an onsen in Taketa. In late November the bamboo light festival is held in Taketa. Streets are covered with small bamboo poles with candles inside them. Lots of Japanese come to visit the village in the evening. Check the website for more info and pictures 
Farm stay aka "Green Tourism" in Shouen Village of Bungo Takada, an old farming village
Showa-machi in Bungo Takada- a town with lots of memorabilia and objects from 1950s Japan
Blue Tourism in Saiki, experience life in a fishing village
Hot springs- Oita is said to have the largest output of hotspring water, there are all kinds of hotsprings from sand, to mud, to so hot they are just for viewing. Beppu and Yufu are main hotspring locations
Water Sports- Water skiing and wakeboarding at Yabakei Aqua Park Nakatsu. Wakeboarding and windsurfing at Sumiyoshi Beach Resort Park in Kitsuki. Ryumon Waterfall in Kokonoe creates a natural waterslide where visitors can raft down the rapids, and even do modest cliff jumping into the main lagoon at the bottom of the waterfall.
Cycling along the the Maple Yaba Cycling Road in Yabakei, Nakatsu (approximately 40km long, camping sites, cycling terminal bicycle rental and accomodations along the trail)
Pleasure Boat on Mikuma River in Hita (operated year round). Eat dinner in perfect Japanese style on a "yakata bune", equipped with tatami mats, paper lanterns, servers in kimono, men rowing the boats, and specialty fish caught by birds.
Eat and Drink
Tempura chicken or toriten and dango jiru (rice dumpling udon soup) are both local specialities. The local fish sashimi is also exceptional here. Two special kinds of mackerel Seki-aji and Seki-saba caught in and around the swift currents of the Hoyo Channel between Kyushu and Shikoku are expensive but exquisite. Also available in Oita, though in rarer quantities than the special breeds of mackerel, is fugu(blowfish), caught by fisherman in the city of Usuki.
The localy famous Barely shochu, and micro brewed beer are well worth a tipple.