There's a nice one that's pretty easy to get to from Incheon Airport.
From the airport just take the 22 bus to the ferry. It takes about 25 minutes.
It will drop you off here:
A return ticket for the ferry costs about W3,000.
You can see the island in the background.
The ferry ride is only 5 minutes. You can see the other side here.
Jump on the island bus when you get off the ferry. Take it for about 20 minutes to the second stop. Jump off and pay W2,000 each for beach access. If you're just staying for the day, that's the final cost.
We stayed for the night, though. A little beach hut costs around W50,000 for the night. We payed up, got the key and looked for our hut, number 20. We found her:
Not too nice...
After a more thorough search we found the new huts:
A lot nicer.
The hosts will give you enough blankets and pillows for 3 or 4 folks. It was relatively clean, and the windows have screens. There isn't a fan, though, so it's stuffy on a hot day.
Other than relax and swim, there isn't a whole lot to do on Muiido.
It's really laid back.
The tide really gets out there:
Next time, I plan to rage it like these guys: