Jeju-do (transliterated Korean for Jeju Province, short form of Jeju Special Autonomous Province) is the only special autonomous province of South Korea, situated on and coterminous with the country's largest island. Jeju-do lies in the Korea Strait, southwest of Jeollanam-do Province, of which it was a part before it became a separate province in 1946. Its capital is the city of Jeju. (From Wikipedia)
Living in Korea, I have not traveled around the country as much as I wanted to. I think it's the same thing for me while living in the Philippines that I didn't travel much. I only went out of town trips with my friends and only when I started visiting Philppines on vacations did I really go to beaches and stuff.
I went to Jejudo on a business trip when I worked as interpreter for a certain Korean actor and it was quite short trip. We didn't have much time to go around since it was all work and in Jeju, to go around, you really need to have a car...
One of the sets of the commercial shot was in Yeomiji Botanical Garden. It was established in 1989. The observation platform with 38 m height in the widely spread field - approximately 134,426 square yard(1 : 3.9537 yd²) and the indoor botanical garden - approximately 15,024 square yard(1 : 3.9537 yd²)- shaped into a sunflower, are proudly known as the largest Botanical Garden in the world. (from the website :D). It was really huge and we had to go from one place to another in a car but the place was really beautiful. I just wished I had some free time to be able to walk around.
Yeojimi Botanical Garden
Another famous scenic spot is, if you have watched Korean drama My Name is Kim Sam-Soon, is the Mount Halla. It is one of Korea's famous mountains and unfortunately I have never climbed it. :(. You can also find Teddy Bear Museum. Dol Hareubang is the distinctive cultural artifact in Jeju. If you ever visit Jeju one of the souvenirs to buy is the mini-carvings :D.