I highly recommend visitor to Daejeon area to visit Gyeryongsan National Park. There are many good hiking tracks in Korea, but in my opinion this park is among the best (for 1 day trips). If you like hiking, there are several peaks one may visit, a good option is to hike from Donghaksa to Gapsa - it'll take about 4-5 hours if you're in decent shape. However, be aware that the path can be a bit rough and you should be in decent shape for it, but if you decide it's too tough, you can always turn back.
The park is also good if you just want to have a day outside the noise of Korean cities. Bring a book and a blanket or get your feet wet in the many small streams in the area. The park also has several nice temples (albeit small).
I highly recommend going there on weekdays as you will have the place almost to yourself.
Entrance fee is 2000 won/adult.
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