We would recommend Roskva's place, we really enjoyed our stay there. Cosy room on the basement of the house with private bathroom and independant entrance, which is pretty convenient ! They were welcoming, even borrowed and fixed their bikes for us, gave us nice tips for places and very good bakery to stop by. Their place is 2 stations away from the airport and around 20 min away from the centre by metro or bus (10-15 min walk from bus 5C or metro station Femoren), but bikes are really more convenient that public transportation if you want to live it as a real Dane ! Would definitely come back if we can.