Take a walk to Grenen, the most Northern point of Denmark where the waves of the North Sea and the Baltic Sea bump into each other. You can walk on the beach with the crowd or nearly on your own via the dunes. Have a nice smorrebrod lunch in the garden of Iscafeen, Skagen.
There is a permanent Street food market with more than 30 street kitchens and bars in an old bus terminal at Ny Banegaardsgade 46. You have a choice between the traditional Danish smorrebrod and many international kitchens, healthy and less healthy.
Both in Aarhus and Copenhagen, we stayed in a Wakeup hotel which is a modern Danish budget hotel. You park your bicycles in your hotel room so better not take the smallest room.
It's certainly worth staying a few days in Copenhagen. With this last trip, we stayed 1 day only as we had been on a citytrip few years ago (most of the photos are also from the previous trip).
For dinner, the Vesterbro area has a lot to offer (we were at Pate Pate). For the healthier choice of breakfast and lunch, Grod is the place to be (we even bought their cooking book).
If you are in to amusement parks, the Tivoli gardens is a must and is the 3rd oldest amusement park in the world (1843)