Don't hesitate : Anne Sofie's appartement is nice, very well decorated, big and quiet. The location is great : even if it's not in a touristic area, it's very close from Copenhagen centre with the bus or the bike and there are shops and restaurants (the breakfast in the cafe located in front of the appartement is very good). And you can reach the airport really easily.
Anne Sofie has been very accomodating (we left our luggage at her place until 6 pm).