Stine's apartment is spacious and beautiful and she's very responsive to messages. Easy to get to/from the airport and central Copenhagen. I recommend renting a bike or using bike share! (I borrowed a Donkey Republic bike from just up the street.) Also be aware that it's a walk-up on the top floor so you'll want to be comfortable going up and down stairs!
The neighborhood has some great parks and restaurants. Definitely make sure to eat at Manfreds, it's quite the experience!