The Dansk Arkitektur Center hosts a permanent exhibition on the development of Danish architecture, alongside temporary exhibits, and features an excellent book- and design-shop. It's fun for kids and the young-at-heart as well, with a 40m-long, spiraling Carsten Höller slide and a playground, as well as a rooftop cafe with views. The Center also runs regular 90-minute walking, running and cycling tours of the city's contemporary architecture.
The Dansk Arkitektur Center is inside the BLOX building on the harbor next to the Black Diamond. If you think its glass-block architecture looks not particularly Danish, you'd be right – it was designed by Dutch "starchitect" Rem Koolhaas.