We had a great week in Copenhagen. The location is excellent in Nørrebro, easily reachable from the airport with a metro+bus combination (or just metro and a pleasant one mile walk past Nørrebro cafés). For kids, there's a playground just across the street.
The place really makes you feel you're visiting someone's home and not a plain rental apt. We traveled with a small kid who was very happy to be able to borrow the toys and books in weird Scandinavian languages. For cooking, there's a proper gas stove. The bathroom is quite small and simple with just enough room to shower in, but that was to be expected in a house from this period. If you want to bathe, there's a public sauna very close by, although not very well open during the summer months.
All in all, our stay was pleasant and we'd definitely consider coming again.