We rented Nanna's apartment during this year's Eurovision. The apartment is nice and cosy and the four of us had enough space. It is located quite centrally, not too far from the airport and close to the city center (Tivoli, etc.).
Nanna is a great host, who even made sure that we had some breakfast food (eggs, cheese, milk, ...) in the fridge and some cold beer!
I can recommend anyone going on a short trip to Copenhagen to stay at her place.