My family and I (2x2) just had a great stay in Elio's apartment which is situated in the best location in Copenhagen.
Cosy side street a block from the main Stroget and too many quality cafes and restaurants to mention. A 7 minute walk to Tivoli was great for the kids and Nyhavn is also only about 10 minutes walk.
The apartment is nice and simple and all you need for a stay in Copenhagen. Elio provides great instructions and tips on visiting Copenhagen.