Appreciate the hushed environment at Namsan Library while skimming over the journals, books and newspapers. See if you can find some board games as well.
This collection of books in Yongsan-gu comes recommended by fellow travelers, so put it on your schedule. However, your day doesn't end there. There are a lot more spots ready for you to explore after Namsan Library. Gyeongbokgung Palace, Dongdaemun History and Culture Park, and National Museum of Korea are close by.
