Despite Copenhagen's reputation as an expensive city, visitors can take comfort in the many free attractions the city has to offer. Things to do in Copenhagen without spending a cent include browsing the exhibits in museums and art museums, kicking back in the sunshine in parks and gardens, and free events and daily happenings, such as the Changing of the Royal Guard or those on offer at amusement park Bakken.
With world class museums such as the National Gallery of Denmark, Statens Museum for Kunst and the National Museum (Nationalmuseet) now opening their doors for free, there's no excuse for not stepping in and learning a thing or two about Danish history and art. Both museums offer great facilities for both children and adults, and are nowhere near as crowded as similar institutions in other European cities. The National Museum also has an out-of-town annex, Frilandsmuseet, which makes for a great family day out from spring to October.
Sightseeing is always free if done independently, including a walk up to Copenhagen's best landmark the Little Mermaid, witnessing the royal changing of the guard at Amalienborg Palace or an excursion north to Klampenborg and Dyrehavsbakken. You can even find free guided tours, courtesy of Sandemans New Copenhagen tours that kick off from outside the City Hall on Rådhuspladsen seven days a week.
Copenhagen has some excellent parks and gardens; one of the largest, stately Frederiksberg Have, has a boating lake and views to the adjacent zoo, while the Botanical Garden is an often overlooked patch of paradise not far from Nørreport Station, with numerous glasshouses should the weather not play fair.