I think it depends on which area you are staying in. Some of the things I was recommend are:
visiting the Gyeongbokgung Palace
going shopping on the Myeongdong Shopping Street
walking around Insadong for culture, food, and shopping
seeing the National Museum Of Korea (apparently it is very beautiful)
and of course, visiting Everland
You can just search the general location of where you will be to find stuff though very easily!