I am a designer living in Copenhagen offering two lovely private rooms at my place (Living room and bedroom with double bed) that are 20 minutes from city center, including 3 min walk to the station.
I am now renting out for my roommates, that went for holidays. Its a beautiful sunny flat (when there is sun in Denmark of course :)) with good location. The only downside might perhaps be an oldish small bathroom, but all else is very comfy :)
Looking forward to meeting you! :-)