Our first Airbnb experience couldn't have been better. It was our honeymoon and first time in Copenhagen.
The apartment suited us perfectly and is very stylish, quiet at night, and was presented very clean and tidy with fresh flowers. The big walk under shower was especially good to have. Our host was friendly and helpful, and even laid on a welcome drink for our special occasion. The only minus point might be that the WC is very small (apparently this is not unusual in CPH) however someone with a very large physique might find it difficult to access.
The apartment was easy to find and only 15 mins walk from the city centre, Tivoli gardens, central station etc. The frequent bus service is useful too (Routes 3a, 6a, 10, 26 all pass nearby)
At the top of the road is the main street Westbrogarde where there's a big supermarket ('Fotex') and some nice nearby restaurants, (We recommend Les Trios Couchons, Von Fressen, Lelé.)
Down the street the other way you soon come to the old meat packing complex also with lots of nice restaurants.
Would definitely go back.