Travel Recommendations for S Korea?

Hello all! Traveling with a friend to south korea in December an curious if anyone has recommendations on things to do! We’re renting a car an location wise going to Seoul, DMZ, Nami Island, Busan & Jeju Island. We’re down for p much anything fun food, shopping, hiking, art, museums, historical stuff, temples whatever! :) if anyone has anything cool (especially on the drive from Nami Island to Busan) that’d be super sick!! :)