I recommend Jeju Time Pediatrics and Adolescent Clinic. I often visit this clinic whenever I need to go to the hospital, and every time I do, the doctors and staff are all very kind. When it comes to vaccinations, I've found this clinic to be more affordable than other clinics. It's located at the Jeju Central Girls' High School intersection, so it's easy to find. Clinic hours are 8:30 a.m. to 6 p.m., with lunch from noon to 2 p.m.