The yellow fever vaccination and certification are done from Monday to Friday (9am to 5pm) at Inchon Airport Quarantine office. Call 032-740-2703 to get an appointment one day before your visit.
You can also get the yellow fever at National Medical Center and Soonchunhyang university Seoul hospital.
National Medical Center open 10am to 11am on Monday and Wednesday, 2pm to 3:30pm on Tuesday and Thursday, 10am to 11am& 2pm to 3:30pm on Friday. Call 02-2262-4833.
Soonchunhyang university seoul hospital opens during weekdays and Saturday morning. Call 02-709-9058 to their international department.
You should get the vaccines 2weeks prior to travel to the endemic area. It is strongly recommended to have live vaccine at the same time or with an interval of 4 weeks between live vaccines.
Other places : http://travelinfo.cdc.go.kr/travelinfo/jsp_travelinfo/ino/inoculate_org.jsp