I would highly recommend staying at Ane/Jens flat. We had an amazing stay here, the flat is lovely and clean. It is just off the metro line from the airport and not far from the centre. It has everything you need. Ane/ Jen were lovely and very easy to get in contact with. We arrived later than we anticipated and Ane/Jens daughter met us at the flat, which was lovely seeing as we arrived so late in the night.
Once again I would highly recommend staying here if you are thinking of visiting Copenhagen.