I recommend Point Dermatology Clinic in Dunsan-dong, Daejeon.

This place is located in Dunsan-dong. It's about a three-minute walk from E-Mart. It's a great location. I went here once to get treatment for a skin blemish, and they treated me well. They disinfected the area, applied a bandage, and explained the precautions thoroughly. They also prescribed topical ointment, which I've been using. I'm completely healed now! Haha.