Ordrupgaard is a beautiful museum with lots of interesting exhibitions. Right next to the museum Finn jul's house is located, a famous danish designer and architect.
A Kilometer stone (circa 1925) stands directly outside Nørreport station, in Copenhagen K. It's easy to pass by, but definitely worth noting if you're in the area — The typographic work on it is incredible.
Cinemateket is a really amazing cinema. It doesn’t show any new releases, but always has an interesting program that takes starting point in either a period in the history of film, a director, an actor/actress or another theme.