I'm very happy i picked Seomun Residence Hotel (written Seomoon Residence Hotel at the hotel itself) for my place to stay in Jeju.
Kind and helpful staff, easy check-in and check out. The room was spacious, clean, and comfortable. The bed was quite hard, but comfortable enough. A big plus was the laundry machine in the room. Location is also convenient for airport, moving around the island, and visiting the city itself.
The only minus I could find was that there were no bath towels available, even by request, only hand towels. So, BYOB (bring your own bathtowel).
If I ever come to Jeju again, I may very well choose this same hotel for my accommodation.