The tallest building in the city is definitely the Christiansborg Tower. Due to this, from the platform at its top, you can see all of Copenhagen, and snap some cool instagram photos. The entrance to the tower is free, but there is a security check, and you might have to queue for a few minutes, and fear not, you don't have to walk all the way up, there is a spacious elevator for the visitors. At the top of the tower, there is also a nice restaurant, with an equally amazing view.