I am a non-recovering travelaholic and love the Airbnb concept, where we can use each others homes when it is not in use. Some of my best travel memories are due to spending time in homes instead of hotels. E.g. sharing a beer with the neighbors on a fire stair in a NY backyard; talking food and vegetables with an old gardener in a lemon orchard at the Amalfi Coast; discussing children and post-war in Croatia with the landlady while grilling squids.
I hope you too will leave Copenhagen with some great travel memories.