In Myeongdong, Olive Young Myeongdong Town (53 Myeongdong-gil) and Daiso

Myeongdong Main Store (43 Myeongdong-gil) are on the same street, so you can hit both. Olive Young is open until 10:30 PM, Daiso until 10 PM. TOCOBO's mini sun stick is just 11g and fits in a pocket.