This was the place I stayed when for 3 nights when I was in Jeju Island.
I would highly recommend this accommodation because:
(1) It is situated at the city centre where you could get access to the shops and restaurants easily.
(2) The hotel was VERY clean and comfortable.
(3) The staff speak English, very helpful and friendly too.
(4) There is a kitchen if you wish to cook (and of course I did not).
(5) There was a (locked) cabinet in the kitchen for Muslim travelers. If I am not mistaken, the previous Muslim travelers have left their uneaten ration for others. Or there could be reserved cooking utensils to be used for Muslims.
(6) Lastly, the price is reasonable.
I would not hesitate to stay there if I have the chance to visit Jeju Island again.