Lone and Michael's place is situated in a nice neighborhood around 15-20 minutes from the center by bus. The room is located in the house's basement and it has a separate entrance as well as its own bathroom. There is also a small hall leading to both the bathroom and the sleeping room. The place is very spacious and clean. The room also has a fridge, and I was surprised to see Michalel/Lone left us a snack and a couple of bottles of water, which was nice.
There are bus stations as well as a train station within walking distance, which should take you to the center fairly quickly. We chose to rent bikes instead, which is a great way to explore Copenhagen. There is a bike shop within 5 minutes of walk, just on the main street, offering bike rental for around 100 DKK per day. But there are plenty of options for renting bikes in the center and price is about the same everywhere.