One of Japan's Three Great Hot Springs, Beppu is also known as the Las Vegas of Japan, a reference more to its extensive sex industry than gambling. The resort has been attempting to clean up its image though, with limited success.
The nearest airport is in Oita, from which shuttle buses run to Beppu (¥1450, 40 minutes).
The Sonic limited express train runs twice an hour from Fukuoka (Hakata) and Kokura, stopping at Beppu before terminating in Oita. If you are coming from Honshu on the San'yo Shinkansen line, switch to the Sonic at Kokura station. From Kokura, you can reach Beppu in 75 minutes at a cost of ¥4290 each way (no charge with the Japan Rail Pass).
An overnight train, the Fuji, runs from Tokyo Station to Beppu in 17 hours, departing Tokyo at 6 PM. If you want reach Beppu in a shorter amount of time, you can take the 10 PM Sunrise Izumo/Sunrise Seto to Himeji, take the San'yo Shinkansen to Kokura, then take the Sonic to Beppu. (12 hours)
The Oita Expressway runs from the south, passing a few miles to the west of the city. Exit at the Beppu Interchange. National Route 10 runs north-south through the city center, along the shore of Beppu Bay.
Beppu's top sight is the seven (or nine) hells (地獄 Jigoku), multicolored volcanic pits of boiling water and mud, and one geyser. The Jigoku are too hot to be diluted into onsen, and they emerge at various temperatures from 50 degrees Celsius to 99 degrees (122 to 210 °F). Some of the Jigoku have a natural smell of sulfur. If you plan on visiting all seven, you can buy a package trip that may save some money.
Downtown Beppu offers several hot springs to visit. You can't wander too far, though, without seeing the equally promiscuous sex shops, which will usually be quite blatant on the streets. If you're going to visit a hot spring with children, and you're worried about this, plan ahead.