Leave your cares at the gate of the fabled Tivoli Gardens at Vesterbrogade 3. While it's a cliché to describe a travel destination as having "something for everybody," here that phrase really fits. The grounds include a Ferris wheel, playground, gardens, lake, beer garden, roller-coaster and numerous restaurants. At night it's lit up with thousands of lights, and you can catch bands, theater performances, comedians and other entertainment. Frequently, the evening ends with a fireworks display.
Watch the Changing of the Guard at noon every day the Queen is in residence at Amelienborg Palace at Amaliegade. Some of the period rooms of the palace are open for public tours.
View centuries of European art at the Statens Museum fur Kunst at Solvgade 48-50. Many of the big names are here: Rembrandt, Picasso, Rubens, Degas, Toulouse-Lautrec, Matisse and Titian. The focus is on Italian, German, Flemish, Dutch and, of course, Danish artists.
Snap a photo of Copenhagen's favorite "resident": the bronze statue of Den Lille Havfrue--the Little Mermaid of the Hans Christian Andersen fairy tale. She's located at Langelinie, beside the harbor. Sadly, she's also a frequent target of vandals.
Rub grubby elbows with the hippie squatters of the utopian Christiania settlement, located in a series of former military barracks off Badsmanosstrede. Here you'll find a typical array of Bohemian arts, crafts vendors and tiny restaurants.
Enjoy your favorite bands at the Roskilde Festival, Europe's largest rock festival, held in late June or early July, a short distance outside town. Follow that up a few days later with the 10-day Copenhagen Jazz Festival.
