We highly recommend Naomi's flat. She is very touching ans her sense of hospitality is unique. The bedroom has a lock, and you will have access to the shared bathroom easily.
The flat is at 10 min (900meters) by foot to the metro station, but is very central. Every touristic places can be visited by foot or bicycle, from the flat.
The breakfast was great.
Regarding the cost of life in Copenhagen, the ratio price/quality is the best.
Thank you Naomi!!