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.
A pretty museum located 30 min north from Copenhagen. It has a stunning sea view and beautiful architecture. Here you can explore many exciting exhibitions. They have a great cafe as well.