There are a wide variety of trails that lead directly out of the city into the nearby mountains. These are not clearly marked, so ask a local or do some exploring.
Mt. Jeoksang
The mountain itself is open all the time, although the road to reach the top is quite steep, and may be impassable at rare times during the winter. At the summit, there's an enormous reservoir used to power the city and a Buddhist temple. Free entry.Firefly Bridge
Located in the center of town, the bridge is decorated with colored tiles, artistic renditions of fireflies, and is covered by lights that change color. Unfortunately, predicting when the bridge will be lit is next to impossible, as it is solar powered and will only light up when the capacitors have charged during special events, however, the bridge will always be lit. Free entry.