I love this little garden for walks... its less busy than Frederiksberg Gardens (right next to it) and Ive been walking with the stroller here endless amount of times
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.
My favorite gallery in Copenhagen, located in the meatpacking area... its great for spotting up and coming talents but also established artists from around the world.
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.