We had a pleasant stay at Sune's flat. The flat was quite spacious and the neighbourhood was modern and felt safe.
The flat is a bit away from central Copenhagen. If you are keen on walking, it is not a big problem, however. We were able to get to Tivoli in 30 minutes by foot.
It should be mentioned, as someone else did in the comments, that the shower is literally in the kitchen. This was not an issue for us but it might be something to keep in mind.
All in all, we are very happy with our stay.