As the summer is my favorite time of the year and that the beach is just 15 min bikeride away, I recommend Amager strand. Full of people usually though, but even so it gives a bit of an exotic touch to such a scandinavian city with the sea and the bright sand in the hot summer days.
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.
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.