Hard to miss this one. Tall, dark, round, huge and really old, Rundetarn is situated in the center of Copenhagen. The Rundetårn dates back to the 17th century and is credited to Christian IV, who built it for the purpose of becoming an astronomical observatory. And observatory it is.
You can access it using a round corridor ramp, with a smooth graduating slope, for a nice view of the city, and an exhibition area. If you got kids who are into Hans Christian Andersen fairy tales, they may recognize it from 'Tinderbox'.