Christiania - they don't like you taking pictures in there and it's known for not being policed so I kept my camera stowed except for photos of the entrance. A few shady people selling drugs and some hippy tat, millions of tourists. I felt like an intruder and left quite fast.
The area nearby is pretty.
The architecture museum on the water is interesting - inside and out.
The black diamond library and the opera are both interesting modern buildings, in general there is a lot of modern architecture to shoot if that's your thing along with more old fashioned things.
We took a boat trip from Nyhavn which covered most of the sites in a relaxed way, not sure if that will be running in December. We also walked to the Mermaid and I wouldn't recommend it unless you want pictures of tourists.
Nyhavn food was viciously expensive even for CP - we ate better and cheaper elsewhere.
The meat packing district is really good for people watching in summer - again not sure about December.
We ate some of the best seafood I've ever had at Kødbyens Fiskebar there - book online if the prices aren't too scary for you and you like fancy food. I did photograph my food
If you're halfway competent cyclist then hiring a bike would be worth looking into - they have a brilliant cycling culture.
I hope you're feeling rich, it made Venice feel reasonable.
Have fun!
The Colour before the storm... Nyhavn, copenhagen by Joe Hunt, on Flickr
Rundetårn by Joe Hunt, on Flickr
