My wife and I had a wonderful weekend staying at Grethe's apartment in Copenhagen.
Grethe is an excellent host, quickly replying to messages and providing us with local information (including recommendations on where to eat), both before and during our stay.
The apartment was really easy to find (Grethe provided us with excellent directions) and is just a 15 minute walk from Nørreport metro station, which has a direct metro service to the airport. Most of the inner city (including the little mermaid statue, Tivoli, palaces, castles etc.) can be reached within half an hour of walking so, for us, the location was perfect.
Inside we found the apartment to be warm, clean and beautifully decorated. The bathroom was a good size (unlike many others in Copenhagen) and our room was very comfortable (the bed was so comfortable that I was reluctant to leave it in the morning!). Grethe told us that we could use the kitchen but we didn't need to in the two nights that we were there, other than to sit and talk with Grethe when we first arrived.
As a summary, I think Grethe's apartment is exactly what Airbnb should be; a clean, comfortable place to stay, right in the heart of the city, with a friendly and helpful host. It will be our first choice if we ever return to this beautiful city.