It is many years since I visited but I don't doubt that Copenhagen is still an attractive place to see. The famous Tivoli Gardens are not to be missed, there are palaces and the Little Mermaid statue which everyone wants to photograph. The city of Odense I didn't find very interesting although it was the home of Hans Christian Andersen and you can still see his house. It also has a popular zoo but I didn't visit either of these. Denmark is fairly flat so much of the scenery is pleasant rather than spectacular, it is nowhere near as attractive as Norway from that point of view.
On the peninsula of Jutland the old town of Ribe is well worth visiting. I didn't get as far north as Arhus and Aalborg, but they are said to have interesting historic town centres.
One of the good things about Denmark now, compared to when I went, is that Jutland and all the main islands are now connected by road bridges and tunnels. There is even a bridge to Sweden, so if you are in or near Copenhagen, you can easily visit the Swedish city of Malmo.
Hope you have a good time. I hope to revisit in the next couple of years.