The headline sights sit within a walk of each other in the centre, but two of the better half-days - the coastal train to Louisiana and the climb up a working incinerator - take you out of it.
Tivoli Gardens
Amusement park next to Central Station, open since 1843, with 29 rides, theatre and around 30 places to eat. The summer season runs 7 April to 20 September, and the park reopens for Halloween and Christmas; entry and ride pass are priced separately.
Ny Carlsberg Glyptotek
Dantes Plads 7, behind Tivoli: Greek, Roman, Egyptian and French collections plus Danish art, arranged around a glass-domed winter garden of palms. There is a roof terrace and the Picnic café if you want a break mid-visit.
Rundetaarn
Christian IV's 1642 observatory tower, climbed by a spiral ramp rather than stairs. Daily 10:00-20:00 from April to September; 60 kr adults, 40 kr students, free under 18, and the observatory itself opens Monday and Tuesday 18:00-21:00 in winter, weather allowing.
CopenHill
Waste-to-energy plant in Amager with a dry ski slope, climbing wall, toboggan run and hiking path on the roof. The rooftop, café, running route and the walk up are free during opening hours; skiing, climbing and equipment hire are ticketed.
Louisiana Museum of Modern Art
Modern-art museum on the coast north of the city, with a sculpture park looking across the Sound to Sweden. Tue-Fri 11:00-22:00, Sat-Sun 11:00-18:00, closed Monday; under-18s free, and there is a children's wing with free workshops.