Reached and checked out of Incheon airport to have quick snacks and got the mobile LTE connection. Our lives really cannot goes on without Internet.
Rented the LG U+ wifi device at KRW 5500 per day. Apparently if you rent it for more than 5 days, the rental for the device is waived if not you would need to pay another KRW 3300 per day for the rental of the device i.e total of KRW 8800 per day.
We booked the domestic tickets (~ KRW 380k for a pair of tickets) from Asiana to Jeju because it depart from Incheon airport. Another option is to fly via Korean Air. Korean Air was abit more expensive ( ~ KRW 550k for a pair of tickets) at the time when i booked the tickets. I believe there are cheaper domestic flights if you enough time to spare to depart from Gimpo Airport. As a kiasi Singaporean, of cause I choose to depart from Incheon! 
Upon arriving at Jeju airport, we took bus 600 ( airport limousine) which is at gate 1. They had huge posters leading us to the bus bay. Each adult ticket cost KRW 5000.The journey took about 1hr and 15 min and dropped off at New Kyungam Hotel and walked to Little France.
Flew from 8am from Singapore and reached Little France at around 2220 (Korea time).
I was too tired and did not take any photos of the hotel room except this un-glam photo of it =x
At USD 80 per night for a “modern” room, It has everything including hairdryer, shampoo, towels and fridge. The room also has a kettle and they have provided instant mix coffee and brown rice green tea. Although it looks old , the toilet and room is clean. I read from one of the comments from Tripadvisor that the bed is very hard ( that’s so true) haha. The hotel is near a lot of cafes , the bus terminal and also Seogwipo Market!
Overall i’m still happy with it as it’s reasonably cheap and good location.
