It really depends on what you are after. Some clinics are better than others for different things.
Here are a few that are considered highly rated for what they specialize in:
Apgujeong Topline Clinic (led by Dr. Sang-Kook Byun, 24+ yrs experience) is one of the highest-reviewed in the area for body contouring and fat grafting.
Relieve Clinic and V Moment are popular with international/foreign patients for non-surgical facial work and both offer English-language support.
BLS Clinic (1,200+ five-star reviews) is frequently recommended in foreigner-focused guides for its one-on-one, non-"factory" approach.