Especially lovely in the autumn, Frederiksberg Have is a really grand park in the middle of the district— Freckled with ponds, streams, and an old palace atop a hill in its centre.

Nestled just north of the city, Dyrehaven is a vast, surreal landscape of meadows, castles, and gnarled fairy-tale like forests — Inhabited by a seemingly infinite population of wild deer. Lovely for runs, strolls, woodland adventures, and the like.

Swimming pool from the 30's. Decorated with mosaic murals by Vilhelm Lundstrøm

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. 

This is one of the places in Copenhagen that I know will do the job if I need some inspiration. The museums’ collections spans from over seven centuries, from early renaissance to current art. Especially the modern collection with its paintings, installations and performance art kickstart the old imagination.  Not only is the collection great, the architecture of the museum is equally beautiful. The old part is a classic museum-building, just as you would expect, but the newer addition is connected by floor to ceiling glass, doing a great job in separating the collections (classic and modern) as it physically changes the context.