My stay at Erik's and his family was exactly what I was looking for: a room in central Copenhagen, within walking distance of the tourist sites, and ease to get to the airport (a bus literally literally picks you up at the front door, the central station is 5min by foot and you can then catch a train straight to the airport in 20min). Erik was very welcoming, and replied straightaway when I emailed the day before looking for a room to stay for the weekend. He was there to welcome me, and provided me with a map of the city and all the info on the main attractions to do in Copenhagen. He had great advice on restaurants to go to as well: i recommend the Obelix cafe (right behind his place) if you're looking for a reasonably priced dinner after a long touristing day :)
His family was very friendly too, and I could use the kitchen for small breakfast and tea, which was great!
The room was very small, but for a weekend alone, it was perfect!
I highly recommend Erik's place if you're looking for a place to stay!