Seoul is where Korea begins, not where it ends.
Most people who land at Incheon spend their whole trip inside Seoul, and I understand why. I have lived here for years and still have not run out of it. But this is a small country with fast trains, and it holds far more beautiful places than one city can show you.
Leave on a morning train and by lunchtime you can be eating fish at the edge of the sea in Busan, with the mountains at your back. A little further and there are royal tombs in Gyeongju that have sat in the middle of town for fifteen centuries, the black stone coast of Jeju, reed beds in Suncheon that turn copper in late autumn, and an east coast where people surf before work. Every region has its own food, its own accent and its own pace, and each one shows you a side of Korea that Seoul never quite does.
I will write these places up one at a time in the journal below: how to get there, how long to give each one, and where the day is best spent. Keep two nights of your trip for somewhere outside Seoul. I hope you leave having seen far more of Korea than you planned to, and that you come back for the rest.
Jisup Shin