6 hours, yes hours, in Southern Denmark

What are your interests and will you be travelling by car or public transport?

Thanks for the response! We will be travelling by car and our interests are largely history and architecture. We are thinking of going to Sonderborg.

A car certainly gives you more options. I'm not sure if Sønderborg would be my first choice, but to be honest I have not been there since I was a kid, so I am probably not the best judge. Just outside Sønderborg is Dybbøl Mølle (Dybbøl Windmill), which is the site of the decisive battle and Danish defeat in the 1864 war against Prussia. It was a pivotal moment in Danish history and the mill itself is a very symbolic site for Danes and something we are taught about in school. I guess it has the same symbolism and meaning as Gettysburg has to Americans. There is a museum about the war and the battle but I am not sure how much is lost if you don't have the whole symbolic and historical baggage that most Danes have.
Another option is the town of Ribe, further north on the west coast. It's the oldest town in Scandinavia, dating back to the 8th century. It has a very atmospheric old town and a Romanesque cathedral. You can climb one of the towers in the cathedral for nice views of the town and the flat marshland beyond.

Thank you Morten we will take you up on your up great suggestion!