I highly recommend Lene's place. It is very close to Amager Strand metro station where if you want to you can also rent a bike. The station is only 8 minutes away from the airport and the city center is less than 15 minutes away. The metro offers a 24/7 service with very little waiting time, pretty amazing. Lene provided us with towels and access to the kitchen to make ourselves coffee and tea. She also suggested to visit Copenhagen street food which is on Papirøn a small island connected to Christiania. There is food over there for every palate! The city is amazing dedinitely worth a visit!