I'd highly recommend Jurate's place. Her spot very close to the city, close to public transportation, and also has a little privacy. We walked to the city and back every day, the commute is around 35 minutes, but a bike is 5-10. You get to experience everything. The neighborhood is great. Some local cafes and restaurants. Jurate was very commutative, thoughtful, and easy to work with. Her place is cozy and very safe. Thanks again for a lovely stay in Copenhagen!!