During our teachers retreat to Ganghwa we stayed at a pension called Marina. It was peaceful and within walking distance of the mud flats. There was a pool, a garden, and at least 1 dog, 2 cats, and 5 kittens. The rooms were very basic, just large empty rooms with a small kitchen, a tv and a bathroom. There was bedding that we rolled out and slept on on the floor. It was nice. Though we did get an early morning wake up of kittens crying outside our door.
Pensions are popular places to stay in Korea, a bit like a guest house. Most of the time you need to know Korean in order to book them.