I stayed 5 nights at Jeanet's apartment with my teenage sons. Everything was perfect. Jeanet was responsive et very helpful, and Heidi, the neighbour that greeted us, was helpuful too ; t.
The apartment is very conveniently located, 5 min walk to Osterport station (trains to Fredericksborg, Malmo, Helsingor, and to the airport too), 2 min walk to the 1A bus that goes across the main attractions of the city ; restaurants and cafes all around, a food store on the corner, and for running addicts, you can run around the lakes across the street.
The apartment itself is really beautiful ; the bathroom is tiny, but the kitchen is huge and so comfortable, and with two bedrooms it perfectly suits a family (beds are very nice too). The heating system keeps you perfectly warm. Jeanet leaves enough room in the cupboards and the fridge for you to put your stuff.
To sum up, you feel instantly at home.