Jeju is a beautiful Island located in the center of Northeast Asia and lies equidistant between South Korea, China and Japan.
It takes only 1-hour flight away from Seoul.From Seoul Gimpo-Airport there are variety of flights per hour flying to Jeju. You can check flight details from Jeju Airline (
http://www.jejuair.net/). You can also purchase a ticket from Korean Air or Asiana Airlines (
http://www.asiana.co.kr/english/ ). Also can compare tickets fare with KoreanAir.
http://www.koreanair.com
If you like cruising (plus are patient person) you can take a ferry as an option however it takes time to get to Jeju. The ferry terminals in Jeju City has daily boats to Busan, Yeosu, Mokp'o, Wando, Noktong, and Incheon on the mainland, as well as several boats to Japan (see the Jeju Port section for schedules). Several other smaller ports have boats to the outlying islands of Kapa-do, Mara-do, Piyang-do, and U-do. Link to check schedule
http://www.lifeinkorea.com/travel2/cheju/116/
The last option is renting a car and then drive!
FYI: a unique immigration policy is applied in Jeju. Chinese tourists, including individual tourists, can go to Jeju for up to 30 days without a visa.