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.
Morgenstedet is vegetarian restaurant located at the free town of Christania, serves the best soups in town and other excellent organic food. Despite it’s name ”the morning place”, it’s also open in the evening.
Just 25 min by train from downtown Copenhagen lies an old and beautiful forest and country area inhabited by wild (but friendly) deer. It's a vast, mysterious space for getting lost in and perfect for spacing out on mushrooms if you bring friends. Stay away on Sundays as it fills up with screaming children and zombie parents. Grab an ice cream on your way back at Bakken, the old David Lynch-ish fairground located at the outskirts of the forest.