Our experiences in Seoul have been generally enjoyable, perhaps due to the fact that we have always had family members to escort us around and translate. If we were to do it by ourselves, I suppose we would manage, but I would certainly allocate extra time to figuring things out along the way. Even after the world cup last year and plenty of english-language schools, we found relatively few people able to converse in english on the street or in shops. The street signs are generally not in english so driving would be frustrating, if not dangerous- traffic is also very, very bad, and the city itself can be confusing, especially in the older neighborhoods. That said, Seoul and the surrounding area can be really interesting and beautiful and the people are generally friendly, especially to foreigners. Korea in our opinion is one of the few places where you can experience the feeling of traveling to a place where western culture has not made significant inroads.
For pointers, I would always carry a map and a description, business card, or address of the place you want to go to. While conversational english may be difficult, more people will understand if it is in written form. I would also try to stay somewhere in Seoul which is accessible to the subway, which we found reliable, clean and relatively easy to figure out.
I'm not sure about Mt. Sorak, but there are several places you should visit in or around Seoul, such as the Korean Cultural Center and Village, the former Palace, the Blue House and of course, Lotte World.
I'm sure others on this site can add to the above.
good luck and enjoy yourselves.