Posted this back in November on the Scandinavia Tips thread (context was my review of Oslo, Stockholm and finally Copenhagen):
Copenhagen - by far my favorite of the three. The city is amazingly beatiful. Food is out of this world. I've never been, but Noma is supposed to be the world's best restaurant. There is a section of the city called "Christiana" (which is a free city I guess?). Basically it's a hippie town on an island in Copenhagen where weed is freely sold/distributed. Interesting place to check out. Also, Copenhagen may be the most bike friendly city I've ever been to. Bike lanes are almost as large as traffic lanes and you can rent bikes literally anywhere. Biking in winter isn't the same as a summer ride around town, but still worth it. Also, I can't remember the name but the main pedestrian road has very good shopping. Also, the women in Copenhagen are the most beautiful of any city I've been to. We would go out every night and every bar and club was filled with gorgeous Danish women.
I didn't put this in my original post, but Smørrebrød, or open faced sandwiches, is ubiquitous and delicious. There is a great restaurant (or at least it was great in '08 when I was there) called Christian 4 tal. Excellent place for lunch. Small place, owner is (or was) there all the time and she'll want to bring you the most delicious Smørrebrød she has. Do it.