Judging by the comments before me, Nana's place is a sure bet. There is truth behind this. We spent an entire week in Copenhagen and we want to go back. Situated by the lake in Norrebro, it's literally a 20 mins walk from all the attractions in the City Centre. With Thai Pan downstairs, Fakta 10 mins away and Netto 4 mins away, you could not ask for a more fantastic location.
The room itself is clean and well kept. The wall paper is beautiful. A candle is left to give it the 'hyggeligt' that the Danish are fondly known for. May I add, I got on one knee and proposed to my girlfriend here so there may be a perceived bias towards Copenhagen, BUT you'll enjoy it. From the living room, you get an exquisite view of the lakes. My girlfriend and I loved walking by the lakes in the evenings. Her suggestions are lovely and the nearby craft breweries are also lovely. All in all I'll be back soon:)