We really enjoyed staying in Kim and Pernille's place - it's outside if the city centre but the transport links are really good, the metro station is very close to the apartment and the tube in to the city centre takes about 10 mins and costs about £2.50 each way which we felt was reasonable. The metro also seems to run all night which is great, we were never waiting long for it. There are some nice cafe/ bakeries close to the house and also a big LIDL supermarket. Our morning routine was to go and get a coffee and pastry and then get the tube into the city to explore!
The accommodation is quite small but more than enough room for two couples, the bedrooms are a good size with a small kitchen and a bathroom. There's a TV with Netflix in one of the bedrooms and a sofa so we chilled in there a few evenings of our stay. The hosts live directly above and the apartment is sort of the basement level of the house - we were concerned that we might annoy the hosts in any way if we were talking too loud but we didn't have any issues! :)
The accommodation is much better value than a lot of the flats we saw in the city centre so I'd recommend it, as you can still see just as much if the city.
Kim and Pernille were kind hosts and mostly left us to our own devices which is fine by us! They allowed us to keep our luggage in the flat until evening on the check out day as our flight was late, which we really appreciated.
There are some amazing restaurants and bars in cph - I recommend Baest for the best pizza you've ever had, llama for south American tapas, and any of the Mikkeller bars for tasty beers!