Accommodation
I have no experience paying for accommodation in Denmark. My time in the country consisted of a hitchhiking trip from one side of the country to the other (the Southern border/Germany to the Eastern border/Sweden). The entire time I slept in my tent in random places, often by the side of the road.
Copenhagen airport is a short walk from the city centre, it is easy to sleep at the arrivals/check in area if you wish to save money on accommodation. I spent one night here despite not having a flight to catch. It served as a good base for the night before crossing the bridge into Sweden the next morning.