Be sure to check the weather forecast before heading to Mt.Sorak because if it's cloudy you won't get to experience a good view. The waterfall hikes are fairly easy, though the hike to the rock is quite a challenge. Oh by the way, there's also the cable car to help you get to the mountain peak.
Seoraksan is the 3rd highest mountain in South Korea, after the Hallasan volcano on Jeju Island and Jirisan in the south. Best time to visit Seoraksan national park is in autumn during the leaf-color change. The scenery at this time in Korea is beautiful!
It costs 3,000 won ($3) to get in Mt Seoraksan Park but if you want to use the cable car to the top of Gwongeumseong you have to pay additional fees. I think it's about 10,000 won ($7)