There's a very good collection of Gaugans and the art museum, which I believe also bears the Carlsberg name. If you are looking to boost the number of countries travelled, you can take the train [from the airport] across to Malmo in Sweden, see a bit of that city, then head back to Copenhagen.

The rest of the suggestions will keep you busy for the time you're there. Do catch the elephant gate at the Carlsberg brewery, while I found Tuborg more homey. The parks are pleasant for sunbathing if the weather cooperates.