The shoe repair vendors on the street are quick and inexpensive and do a fine job doing minor repairs in my experience. But for more extensive repairs on pricey shoes here is what I found by searching the Korean internet portal, naver.com for 명품 구두수선 (luxury brand shoe repair).
A blogger posted a list of repair centers she saw in a magazine which appears to be quite recent (
http://m.blog.naver.com/PostView.nhn?blogId=ibbino1&logNo=20133334489&categoryNo=0¤tPage=1&sortType=recent Korean)
Heres some info from it:
The magazine it came from is called Singles.
First of all, there is no official repair center in Korea. To service the demand, private companies have been created. Even if you give your items to one of the big department stores in Korea, they will just outsource to one of these companies.
Name: 영일사 (youngilsa) specializes in leather shoes and Uggs boots
http://youngilsa.co.kr/Address: 서울특별시 강남구 신사동 658 현대로데오상가 145호 #145 658hyundai rodeo sangga Sinsadong Gangnamgu Seoul
Phone: 02-547-4959
Name: 이화사 (Ehwasa)- Repairing leather shoes for the past 40 years
Phone - 02-3277-4864
Location : 이화여자대학교 내 inside Ewha womens university
Please note that since Korea is a Korean speaking country, the likelihood of someone being able to understand you on the phone could be slim. If your language skills are weak, Id have a Korean speaking person call ahead for you.
The rest of the places on the list are for luxury handbags and jeans so I didnt bother translating for you.