The city museum is in an old mansion house, west of the Central train station -- a bit of a walk from the old town, but worth the trip, I think.
The museum is a bit confusign in layout, but in general there are exhibits on the history of Copenhagen from it's founding to the last decade with lots of displays of old stuff from the excavations of the city, tons of photographs, and collections of modern pieces that show the evolution of Copenhagen from a port city to a medieval power to the modern day. A bit hard to follow, since timelines and explanations of the history are mixed in with displays of typewriters and record jackets but it's a very neat museum.
They also have a high-tech multimedia exhibit on "being a Copenhagener" which we were engrossed in for a long time. Interviews, movies, letters, personal histories and artifacts with immigrants to Denmark and what it means to be a Copenhagener -- focusing a lot on recent immigration from muslim countries, and the history of integration in the city. It was fascinating to see how non-Danish saw living in Copenhagen and how it affected the city.
Nearly everything has good english notes,and where they are no on the labels themselves, a book/sheet is available in the room to decipher things into English or German. I would have liked to see more about the founding of the city, but the approach the museum takes to history is a good one: following the change from a "king-as-god's-emissary" absolute rule to democracy really does illuminate the changes in the city.
Definitely worth an hour or so if you are interested in another view of Copenhagen.
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