I recommend Seomyeon Jaylin Dermatology Clinic.

Jaylin Clinic is considered the most famous dermatology clinic in Seomyeon. It's located in conjunction with a plastic surgery clinic, and Jaylin Eye Clinic is located across the street. Located inside the Samjeong Tower building, it's easy to find. Every time I visit, there are always a lot of visitors.
They offer a variety of treatments, and their prices are reasonable. The hospital's facilities are also fantastic. The doctors and nurses are friendly, so I highly recommend them to anyone looking for a dermatology clinic in Busan.