The west coast is not the east coast. The sand is greyer and finer, the water is shallower and murkier with silt, and the tidal range is enormous — the sea can go out several hundred metres. What it gives you in return is water that is genuinely warm by August and sunsets straight out over the sea, which the east coast cannot do.
Daecheon is the biggest and best-organised of the west-coast beaches, about three and a half kilometres long with a full seafront of hotels, restaurants and arcades behind it. Boryeong is a straightforward two hours or so from Seoul.
If you are coming for the mud festival, understand what you are signing up for: it is a genuinely large, loud, crowded event aimed squarely at people in their twenties, and Daecheon in mid-July bears no resemblance to Daecheon in September.