We have just returned from a stay at Gitte's wonderful apartment. The location is perfect; it's about a 15 minute ride on the metro to Christianshavn station, then the apartment is about 3 minutes away by foot. To walk into the centre to see the sights takes 10-15 minutes.
The apartment itself is great - clean, tidy and cosy (not in a small way!). We really did enjoy coming back to relax after a long day sightseeing before heading out for food. There are plenty of cafes, bakeries, restaurants and small supermarkets nearby. We recommend Lagkagehuset for some Danish pastries. Closer to the centre, try Cafe Norden for a fantastic brunch or breakfast.
Gitte was an excellent host and very responsive to our questions. We wouldn't hesitate to stay here again if we return to Copenhagen.