I recommend Severance Hospital located in Sinchon-dong, Seodaemun-gu.

You probably know this is a very famous hospital. Many medical students from Yonsei University go here for internships and continue their careers as doctors. It's no exaggeration to say that Severance Hospital is home to some of the most talented doctors in Korea. The department I visited was plastic surgery. The doctor I met was very kind, so I was able to receive excellent treatment and schedule my surgery.