Me and my boyfriend had a great stay at Lene's play. It is really cost and homely with everything you would need for a comfortable stay in Copenhagen.
Lene was very accommodating meeting us later than expected when our flight was slightly delayed and letting us stay a little longer after we had done the marathon, for which Lene's place is perfectly located.
It is easy to get to from both the airport and the centre and there are some great bars, restaurants bakeries on the streets around.
I would more than recommend Lene's place!