There is enough going on in Sonderborg that you can easily be satisfied by the events in the area. However, every so often you need that change of scene. A good way to get that is to get yourself to one of the bigger cities around.
Copenhagen is an excellent place to spend the day exploring, without losing out on the comfort of your own bed in Sonderborg. This is my favourite way of spending a day in Copenhagen.
Get the train at 5:53 from Sonderborg station. If I still have some sleep to catch up on I can easily get it on the train, especially since this train is rarely too busy (especially up to Odense).
Arrive in Copenhagen at 9:50. This is perfect timing as it is right around the time when things start happening.
Drop in to the National Museum. The best thing about this museum is that it is free, so you don’t feel the need to do it all at one go. I typically pick one of the exhibit, from the olden times to the year 2000, and check it out. There are often special exhibits, so there is always something new to see.
Time for some relaxation. Walk down Stroget, the long shopping street through Copenhagen’s centre, to Nyhavn. There pick up a pølse from one of the sausage stands, some beer, and get your tickets for a boat trip to sight-see from the water. A good way to relax for 1h while still seeing the town.
At this point there is a couple of options:
By now you are probably quite hungry. Go down to Strædet (Kompagnistræde and Læderstræde running parallel to Strøget to the south) and pick one of the numerous restaurants for a relaxed dinner.
Finish off your day at Tivoli. You can also opt for dinner there, or go there directly after the boat ride for an afternoon of fun, games and entertainment.
Catch one of the last trains from Copenhagen back to Sonderborg. By now you are probably quite dead. Enjoy your slumber for the 4hrs or so it takes to get to Sonderborg.