Copenhagen is a wonderful city. Highly recommended is the Resistance Museum in Churchillian Park. This is a fascinating museum which tells the story of Denmark's remarkable resistance to the Nazis during WWII. It is not very big so you can see the entire museum in about an hour and a half.
Also, do not miss Fredericksburg Castle which you reach via a 20 minute train ride and a short bus ride.
Also highly recommended in a canal tour on boats that leave from Nyhaven (this is a restaurant/hotels/shopping area in Copenhagen)
Be careful of the bicycle riders when you step off the bus.