Christiania is a ‘must visit‘ in you are in Copenhagen. I personally like go for a walk , visit the many restaurants or coffeeshops, or  explore  ‘Den Grønne Hal’ for use construction materials

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. 

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.

A Kilometer stone (circa 1925) stands directly outside Nørreport station, in Copenhagen K. It's easy to pass by, but definitely worth noting if you're in the area — The typographic work on it is incredible.

This is a lovely place to go if you want to enjoy the beach. It's also beautiful when its not bathing season. Go check out these little beach houses in beautiful colors. Also make sure to go for a walk in the forrest just next to the beach.