We spent five nights with my family. It took only about 15 minutes by a taxi from the airport. The room was easy to find. The metro station was 15 minutes away on foot. It was a little far with two small kids, but there were many shops and cafes near the station so it was good to walk around. Buses were useful to the central Copenhagen.
The apartment was clean and beautiful. From the kitchen window, we could see the lovely inner yard. One day, two rabbits were there in a circle, and my kids patted them.
We could totally relaxed in the apartment, more private than stying a hotel.