Welcome to Muuido
If you’re looking for a beachside escape within easy reach of Seoul, the tiny island of Muuido (무의도) fits the bill. Broad stretches of golden sand and forested walking trails are just a short ferry hop away from more developed Yeongjongdo (home to Incheon airport). A road bridge was under construction at time of research, however, so you might want to get there before the developers do.
Note also that swimming is only possible during high tide; at low tide the water recedes substantially, turning the area into mudflats.