Copenhagen is an ideal city for walking. All of the historic sights are clustered closely around the city center. Sidewalks are plentiful and in good condition, and there is nowhere better for pedestrians than the Stroget. In fact, we walked everywhere we went within the city. The longest distances are only about 3 km: from Christianshavn to Rosenborg Slot and Tivoli to the Kastellet! We never bothered with a taxi, train, or boat, except when we left the city.
For the inner part of the city, I guess, walking is the best and most competitive option. And that is also how you get to know the city quickly...