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.
A lovely co-working space & café, in my favourite neighbourhood in Copenhagen. The community here is warm & welcoming, and the space itself is a dream. Hardwood floors, dusted gem-tone walls, designer furniture, Depanneur coffee, and great lighting in a period building. If you're freelancing within the city for the long-term, or for the short — I'd wholly recommend having a visit.