Here is where I got a 60$ round-trip flight from Seoul to Jeju. Make sure your ticket says the name on your passport. Talk to agents at the airport if any problems arise, and arrive early for less hassle. Keep luggage locked up in Seoul if you have too much.
Waterfront View, Cafes, and Convenience Stores within walking distance. Quiet area and private Jacuzzi Tub. The host has multiple homes.
Greem Cafe
Flying Aewol Café
Eomjaenge 1988 Dessert Cafe