If you wanna shop for your own clothes , check out following:
Miliore, doota, and APM
You can bargain hard at these malls it's fun ! And they got some great quality stuff
Other big malls like hyundai, shinsegae, Lotte and etc are for brand names
For socks, gloves, scarves , undies , check out pyunghwa market ( you will get above 20k steps if you can go through all the floor levels from end to end )
This place is a whole sale place so, they might ask you to buy more than just a couple of items.
For jewelry, go to jewelry district in jongro.
They are probably the biggest wholesalers in SK. If you have big hands like me, you won't be able to get something on the spot so they will require about a week. ( Pro tip: if you are planning on buying gold , go to jongro first to order before your trip ends)