Seogwipo, a more upmarket and tourist oriented city on the south side of the island and home to the Jungmun Tourism Complex.
Alternately, use Jeju City as a base to explore the island's interior and attractions:
Mt. Halla, Seongsan Ilchubong and Manjangmul Lava Tube, the three UNESCO rated natural sights of Jeju.
Loveland, the infamous themepark in central Jeju.