Gatbawi is a pair of tidal rock formations on Mokpo's eastern waterfront, named because they look like two people wearing gat, the old Korean horsehair hats. The formations are not huge, but the boardwalk makes the visit pleasant, especially in the evening when the rocks and water are lit.
Combine it with the nearby museums rather than crossing town only for the rocks. As a cluster, Gatbawi Culture Town fills a good half-day.