I will truly recomend Jonas' apartment. The location is perfect, you can walk to the city center. The Nørrebro area is hip and trendy with all the shops and restaurants nearby. We spent 4 nights with our 1,5 year old daughter, and she loved to play with "new" toys during her stay! There are several things to do with kids just around the corner. "Den bemannede legeplads" for instance, is 500 metres away. Here you can meet and cuddle with rabbits, chickens and goats.
The only thing I wish was a little better is the cleaning. Besides that, the place was perfect, and we would definitly rent the apartment again.