I recommend Jeju Time Pediatric Clinic. I often go to this hospital when I need to visit, and every time the doctors and staff are all kind. When I look for vaccination clinics, this hospital is also more affordable than others. It is located at the Jeju Jungang Girls' High School intersection, so it should be easy to find. The clinic hours are from 8:30 AM to 6:00 PM, with a lunch break from 12:00 PM to 2:00 PM.