This wonderful apartment is right in the middle of everything. You can easily walk to Tivoli or the Zoo; it just takes 20 or so minutes. Right around the block you find many corner stores, restaurants, bars and so on. The overall vibe is progressive / alternative.
The apartment is very personal. This is the private home of a family and not a sterile for-profit rental. This makes the stay so much more welcoming.
Henrik and Mia give many good tips on what to do in the city!
One more thing: if you come by car, get a parking permit for the blue zone from https://www.kk.dk/parkering (time of this writing is August 2021, your milage may vary). This is a digital permit and will be issued within a few days. It is much more cheaper than paying through any other means.