The Copenhagen Card, which costs about $21 for one day, $33 for two days, or $45 for three days, is a real convenience. It allows the use of transportation and free admission to many museums, palaces, and other sights, and it can be purchased at the airport. I got a three day card after arriving at the airport at five in the afternoon. That gave me that night, the next two days, and until five on the next day.
The word "Copenhagen" is used very loosly in the name of this card, because it also includes suburban trains for forty-five or more miles into the countryside, and admission to places such as Dragor Museum, south of the airport, Roskilde Museum, which has Viking boats, and Frederiksborg Slot and history mueum, about forty miles north of Copenhagen. Buses in these towns are included, also. To make the best use of the Card, plan a five day stay with three days (spread over four, as it is really 72 hours) when you use the card, then the rest of the time for shopping and Rosenborg Slot and other attractions which are not included on the card.