Cheongju is a city of roughly 600,000 people, and a number of quite interesting things to see and do.
Every second year, there is the Cheongju International Craft Biennal, which features amazing folk crafts from countries all over the world (this year featured Russia, China, Japan, Vietnam, Great Britain, The Phillipines and others), most of which are for sale. The most amazing thing on display this year was a queen size bed made entirely out of jade, and ornately carved, for sale for the low low price of 30,000,000 won (roughly $30,000 USD).
The city also features an intriguing traditional covered market downtown selling all manner of wares, from de-boned pig faces to plastic toy swords to live eels, and a maze of walking streets lines with shops of all description.
There is an iron flagpole centuries old that marks the location of an old buddhist temple. The temple is long gone, but amazingly the iron flagpole remains. It is, contradictorally, located right behind the modern Cheongju Department Store, and apparently features the best place in Korea to get dokboki (rice cake things swimming in medium-spicy sauce) - at least, according to the locals!
There is also the Cheongju Early Printing Museum. Cheongju is birthplace of the earliest known book printed using movable metal type. The book's short-form name is Jikji, and is a sort of mascot for the city. While the book itself currently resides in a French museum, the equipment and details of the moveable metal type printing process are available at the museum in Cheongju.
Cheongju is also located conveniently in the central area of Korea. From here, you can take a bus to Seoul (90 minutes), Daejon (30 minutes), Pusan (4 hours) or a number of other important destinations. It is a clean and exceptionally safe city, and has a number of good bars where the foreigners like to hang out, in the university sector. Attic Bar and Pearl Jam are two of the most popular.