Anja' s husband Florian was at the apartment to meet us and go through a few things. He left us a good list of places to eat and things to see. The apartment is as shown in the photos - very cool scandinavian design, and in a very quiet location. It's on the 4th floor, so not suitable for those with walking difficulties. It's also about 7 mins walk from Nordhavn station which is only 2 stops from the centre.
The walk into the city centre is about 35/40 mins, although you can reach the botanical gardens in about 20 mins.
We tried the Halifax burger joint which was very good and only 10 min walk. As for bars in the area, there aren't many and I wouldn't bother with the Irish bar nearby, it's a smoking bar and is absolutely unbearable.
Definitely a great base to spend the weekend exploring this great city. Would come back for sure.