The apartment is wonderful, with some great cafes nearby (Mad & Kaffe and Brod in particular are ones to check out!) The 1A bus, which can take you to Tivoli/Glyptotetkt/National Museum and the city centre is about <1 minute walk away and there is a bus around every five minutes. It's also only 15 minutes walk to get to the train station, making it very handy to get to/from the airport or to take a trip to Malmo like we did). It would only take around 20-30 minutes to walk into the town centre too if you wish. We had a great sleep every night as the neighborhood was so quiet. The area seems to be mostly students and young professionals - it felt very safe to walk around, even late at night.
Mette answered all our questions and gave some great recommendations. If we ever go back to Copenhagen, we'll be sure to book with Mette again!