Well, WAY back in 1984 I was in a music group doing a tour of the country. All I remember is Skagen (which I loved!) and driving the countryside of the Jutland peninsula. We then took a ferry to Sweden.
Then, with my fond memories of that trip years back, I went again in 2005. I rented a car in Copenhagen, spent a week driving from Zealand across Fyn to the Jutland again, and drove all the way up to Skagen again (and loved it again!) Then I drove back to Zealand to visit my friends (who live outside of Ringsted). They have family on Bøgø and Møn (I CAN say both of the names of those islands accurately) and we drove around a lot and did some exploring (chalk cliffs....) It was a blast!