Jens' apartment really made our trip to Copenhagen memorable. It's in a perfect location and within easy walking distance of great shopping, restaurants, bars and the train/metro. His place has all the amenities you need to set up shop for an extended stay and the roof top deck is..well..it's pretty awesome. We had an amazing time sitting up there watching the city come to life each morning.
Only drawback was the stairs to apartment as there's no elevator. Wouldn't recommend to those will small kids (strollers) or struggle with mobility (elderly).
Otherwise, I can't imagine a better set up to help you discover Copenhagen!