A contemporary art exhibition space located right next to Østerport station, they have a nice little visual arts bookshop as well.

Copenhagens bikelanes is all around the city. Its one of the best cities in the world to get around on bikes, there is even free bike servicestations around town:)

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.

Contemporary Art Gallery in the center of Copenhagen focusing on mainly international, abstract, minimalistic art. 

In the summertime you can take the Metro directly to the beach. And if you're over the crowded white trash tanning and blanket sex scene, enter the hidden away mens or womens area located in the big wooden beach bathhouse. Here you can lie naked and enjoy the sun on your private parts while reading a novel or surfing your iPad. Expect lots of gays and lesbos which can be a curse or a party depending on who you are as a person.