For routine stuff, a lot of people have better luck with neighborhood 내과 or 이비인후과 near a university or office area instead of jumping straight to an international clinic. In Korea, Naver Map reviews usually tell you pretty fast whether staff can handle basic English and whether NHIS pricing is explained normally. If the desk looks confused, I ask for the 예상 본인부담금 before treatment so there are no surprises later.

If you are in Bundang, I would also check clinics around Seohyeon or Jeongja rather than only the expat-famous places. In a lot of Korean neighborhood clinics, the doctor is fine but the front desk is the bottleneck, so I usually call first and ask whether they can explain 국민건강보험 price and prescription steps in simple English. That one phone call saves a pointless trip more often than people expect.