I'd always recommend staying at alexandras! Her flat is very clean and lovely it's also about a 30 minute walk away from the center. She wasn't there when we arrived but she sent over a friend of hers who welcomed us and showed us the flat. During our stay Alexandra asked me a few times if everything was alright. When we left Alexandra came over and let us out.
Me family and I really enjoyed being in kopenhagen also because of the flat we stayed at:)