Grabel Hotel Jeju 

This is a beautiful hotel. We were thrilled to get a seaview room on the 7th floor to watch the fishing boats. The pool is about 37 degrees C so you can stay in it forever. Towels cost 3000 won so most people just used the robes supplied in the rooms. It is about a 7 min walk to a rocky, very scenic beach. Cab from the airport was only $7 US. We otherwise rode buses from the stop in front of the hotel or one a block south. There are interactive signs in the bus stops that show in English when the next bus arrives. Buy a T-money (or equivalent) card in any convenience store and you don't need to worry about having cash. Most rides cost us barely over $1 US. Sandy beaches would be about a 10 min bus ride in either direction. We had to go into Jeju City to rent bikes (about a 30 minute bus ride) but loved our ride - we did the coastal route heading west (past our hotel). The trail is sub-optimal in a few places (you ride through bus shelters) but incredibly interesting. We initially tried to rent a bike on a Wed and it seems many of the shops close that day. We eventually went to Tourist Information and they helped us find bikes for the next day. However, had we phoned enough shops, we probably eventually could have booked on our own. We paid 25,000 won for MTB bikes and 50,000 won carbon fiber. Helmets were decent. The restaurant towards the beach with the windmill that you can see from the hotel was excellent and they tried very hard to ensure that we knew what sauces to use on the Korean food that we ordered. Pattyster (south of the hotel) has superb hamburgers.