Jeju Island at the southern tip of South Korea is a beautiful place. It's good for vacationers and tourists.
As for English education, it is much like the rest of Korea. If you are lucky enough to sign up with a reputable school, you will love it. If not, and this is most likely, you will hate it and leave with a bias and permanent bad memories.
If you do go to Korea, make sure you are properly enrolled in the National Insurance Program, because if you get sick or injured, without medical insurance, you will know hell on earth.
My advice: keep searching the Net as you just did and try Taiwan, not Korea and avoid Ulsan at all costs.
Good Luck
A N E T