Tivoli Gardens, just behind Copenhagen's Central Station, has been open since 1843 — one of the world's oldest amusement parks. It is not a theme park in the modern sense but something more interesting: a pleasure garden with rides, restaurants, concert halls, pantomime theatre, and thousands of fairy lights, all within a beautifully landscaped setting of lakes, flower beds, and ornamental buildings in a vaguely Oriental style.
Tivoli works during the day and is genuinely magical at night, when the lights come on and the atmosphere transforms. The rides range from the vintage wooden roller coaster (1914) to modern thrill rides. The food is better than you would expect from an amusement park — several proper restaurants and a range of cheaper options. In summer there are free concerts most evenings. The Christmas market version (November–December) is excellent.