The key is not to try to “do all of Seoul” between shopping stops: leave one neighborhood per day and allow time to test shades or compare prices. A comfortable itinerary would be:

• Day 1 — Myeongdong + Namdaemun: beauty stores, Olive Young, and Korean brands, with breaks for food. Compare the same product at a couple of stores; promotions and stock vary quite a bit. Save your receipts if you plan to apply for a tax refund, and confirm on the spot whether the store participates and what documents you need.
• Day 2 — Seongsu + Seoul Forest: boutiques, pop-up stores, and cafés. It’s the most fun day for discovering brands, but pop-ups can be short-lived: check their official accounts before making a detour.
• Day 3 — Gangnam: COEX and the surrounding area for indoor shopping; add a visit to a large beauty store if you’re interested in comparing lots of brands in one place. Hongdae is also a good alternative if you prefer clothing, youthful stores, and a nightlife atmosphere.

Useful phrases: 이거 테스트할 수 있어요?(Can I try this?),​면세 돼요?(Can I get a tax refund?) and​재고 있어요? (Is it in stock?). If your flight leaves early, save your shopping for the day before, not the last minute.