I am currently studying in Copenhagen and have to say that the city is alive and booming with the wave of spring weather coming through. The main pedestrian walk, dubbed the "Stroget" is great to stroll through on a warm day to find some great shopping. New Harbor, they call it "Nyhavn", is picturesque of what you would imagine in a European town with a great canal tour for only about 10 bucks. Seeing the Mermaid is no spectacle, but there is plenty to see and do here around the summer. Great blend of cultures, perfect cafe atmospheres, and altogether great people with excellent English skills. Everyone speaks English here so it makes the trip that much easier. Hope this helps.
I know what you mean about growing trips! I have added Slovenia and Romania to my "see if I make it" list.
I've never been to Copenhagen, but I want to just to see Christiania: http://en.wikipedia.org/wiki/Freetown_Christiania
Ajovens, have you been there?