I recommend Seoul Yeon Dental Clinic in Sangnam-dong.

I have been going to Seoul Dental Clinic for two years to get orthodontic treatment. The dentists are very thorough and careful♡ The nurses also take care to ensure the treatment is painless~

I went to have my impacted wisdom tooth removed, and they did a great job! The price is also the average cost you'd find at a typical dental clinic^^ I think it would be good for you to visit once~