I loved Muuido when I was living in Seoul. I went a few times over the summer and in the late fall with friends and loved it. Bring food to grill or a picnic, reserve a bungalow and spend the night! You can buy beer on the beach but they often run out and are pricey. You can see some of my photos here https://livetravelteach.com/muuido-island-the-perfect-getaway-from-seoul/