What's the must-see thing in Copenhagen?

Everyone asks about the Little Mermaid first. The Edvard Eriksen bronze from 1913 sits on a rock at Langelinie pier, measures about 125 cm tall, and draws a permanent crowd of selfie-takers at any hour. You can see the whole thing in 10 minutes. But Tivoli is the real answer, and it's not close. The park predates Disneyland by over a century. It opened as a pleasure garden with rides, a theatre, and restaurants, and that formula has barely changed. The air inside carries the smell of caramelised almonds from the corner vendors. Lights string through the old trees above Tivoli's boating lake. Rides cost 30-80 DKK each, or pick up an unlimited pass for around 250 DKK. The park closes between seasons. It typically shuts after September and reopens for a Halloween run in October and a Christmas market from mid-November through late December.

Rosenborg Castle is the second stop. Christian IV built it as a summer house in 1606, and the basement vault holds the Danish crown jewels, including Christian III's 1551 coronation sword. The room below Christian IV's great hall is cold and dim, with the faint mineral smell of old stone. Tickets run about 130 DKK, and there's rarely a queue before 11am. The castle connects to the King's Garden, which is free to enter. In July the lawns fill with Danes on blankets, eating open-faced rugbrød sandwiches and drinking canned Tuborg. The walk from Tivoli takes about 20 minutes through the garden, so these two fit naturally into a single afternoon. The interior has 17th-century staircases and low ceilings, difficult with a stroller. The long gallery on the top floor holds royal portraits going back to the 1400s.

The Ny Carlsberg Glyptotek rounds out the three. Carl Jacobsen, of Carlsberg beer, founded the museum in 1882 and filled it with one of the largest Gauguin collections in northern Europe, alongside an Etruscan wing that competes with anything in Rome. That said, most visitors to the Glyptotek remember the winter garden more than any single Gauguin. The glass-domed atrium in the building's centre is warm and humid, a 19th-century greenhouse full of palms and the sound of water hitting stone. On a grey Copenhagen afternoon, that room changes your entire mood. Free entry on Tuesdays. Other days run about 125 DKK. The museum sits on Dantes Plads, a 5-minute walk south of Tivoli.

Timing matters more than ranking in Copenhagen. The city currently sits around 20°C in late July with partly cloudy skies, and the light lasts past 9:30pm, so you can fit two of these three into a single afternoon without rushing. Christiansborg Palace and Amalienborg are both solid second-day options, but neither earns a spot in the top three for a first visit. The Christiansborg tower has a free observation deck with the best overhead view of the city's copper-green roofline. Skip the Nyhavn canal boat tours. They cost about 100 DKK for 60 minutes and repeat the same circuit between Christiansborg and the Opera House.