Oedaldo was great, until they put a waterpark on the island and brought boatloads of people over. They neglected to renovate the bathrooms, however. Still, outside the "swimming season", it's a great place that's close to Mokpo.
Myeongsashimri in Wando rocks... but maybe just because of fond associations I have with the place - camping weekends, afternoon walks, and surviving a typhoon that had me doubting that I would actually survive.
I think Korea's beaches are, in some cases, their undiscovered gems. I certainly wasn't expecting to find myself beaching it up when I first arrived.
I'm sometimes shocked and saddened by the state of some beaches here. Plastic bags blowing around (I mean... please! Think about the marine life!), broken bottles...) and always try to follow the basic campsite rule and leave it in better shape than when I arrived. It does depend on the time of the year, however, and whether anyone is assigned to actually clean the beach.
And I will never ever ever get used to seeing people swim in jeans and hoodies. If you aren't wearing as little as possible on a beach, then you're wearing too much.