If you are interested in museums, Louisiana is a short train ride away and easily spend a day at the town, museum (short walk from the train station) and the surroundings.
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I’d probably go to the National Museum and walk past the royal palace over to Nyhavn and have lunch at an outdoor restaurant by the water. Water tours are nice there, too. |
Meant to add that the Tivoli gardens are right by the train station, and so you could walk around & get lunch there. |
We did a great food tour— walked all over the city and got try lots of things. Would be my recc for how to soend a few hours. Then you could finish by seeing the museum or just walking by Nyhavn down to the little mermaid statute. |
A week is not that long. Take the train up to the Viking museum one day, go to that famous castle another day, one day in Malmo, another day doing cophenhagen proper and the amusement park… week is gone. |
I wouldn't bother with Malmo. Just spend your time in Denmark. |