Jeju-do is worth visiting for at lest a couple of days - hire a car, its very cheap and the only real way top get around - no more than $30 a day and using natural gas, so the cost of running it was not too high either. I LOVED Gyeongju, Seoul and Hallasan NP.
only part of it, takes an hour at most if memory serves me correctly. The floor was wet and uneven, but not difficult in my opinion. Still better to wear walking shoes if you have them- are you going?