National Science Museum
Showcases both pernament and special exhibitions.
Daejeon Balloon Festival
Once a year around October, this is not the international balloon festival you are likely thinking of. The 2010 edition of this annual event had a sum total of two hot-air balloons, both tethered tightly to the ground. However, as the sun sets, they let off an amazingly large quantity of small disposible lantern balloons that float off in the south-westerly breeze of the neon Smart Towers housing complex and into the mountains. Both Daejeon city and the DICC have a tendancy to try and book in other festivals at the same time as this nearby to attract more out-of-town visitors, so keep an eye on local schedules.
Daejeon Observatory
Here you can observe the sun during the day or any number of celestial bodies at night. Located west of Expo Park, take the 604 bus to the observatory stop. Open from 2-10PM, closed Mondays and the day following a national holiday.
Daejeon Currency Museum
Historical currencies of Korea up to the modern day, including those of the DPRK North Korea.
Uam Historical Park
Historic scholarly site nestled in a mountain valley. Has a well kept lake and quite nice to stroll around. Hosts a poorly gazetted festival sometime in October. For hikers, the trail hidden at the rear-left of the park continues up the mountain, past a place to fill your water bottles and after a less than 30 min walk, all the way to the top of the ridge overlooking the immense Daecheong lake east of town.
hike
Any, or all, of 5 mountains designated by Daejeon tourism amongst the city's eight most popular sites:
Mt. Sikjangsan southeast
Mt. Bomunsan south
Mt. Gubongsan southwest
Mt. Jangtaensan south
Mt. Gyejoksan northeast
Most have either a typical Korean gazebo at the top or a historic fortress wall, or often both. Jangtaesan has a treetop walkway. Springs offering drinking water are marked on the local maps. To find the start of the myriad hiking trails, a good rule of thumb is to look for burial mounds on the hills, as they are often lurking just behind them. Once on the trail, trail marking and intersection signposting is really good, but the actual start point locations are almost never announced.
Theme parks
Expo Park
Located in north Daejeon and site of the Taejeon Expo 1993. The city still holds great nostalgia for this place and as such, the now rotting plastic mascots feature heavily all over the city, even on the manhole covers. It's an eclectic mix of science exhibits and disused halls with an out of place outdoor art plaza near the center that even has a bit of now heavily graffitied the Berlin Wall. One of the buildings looks a bit like a Sandcrawler from Star Wars. Also contains the funky "year 2000 as imagined in the 70's" style Hanbit Tower. Enveloped in the far north of Expo Park there is a separate but small theme park called Kkumdori Land complete with a small roller coaster, although it's primarily oriented for kids.
O-World
Another theme park, this time on the far, far south end of the city. Comprises Zooland zoo boasting 130 species, Flower Land flower park boasting 190 species and Joyland a regular ol' themepark. Easy to reach if coming by car: literally all major intersection signs across Daejeon point to here. By bus, you want the 301, 115, 311, 314, 318 or 315.
Note that the Dreamland theme park up on Mt. Bomun, despite being marked on many maps is long since gone and the equally well known abandoned site also recently completely bulldozed.