What to do in Copenhagen when it rains

Copenhagen is a city people plan to walk, and that is exactly why a grey morning catches so many visitors out. The centre is small enough to cross on foot in half an hour, so the usual plan is a string of outdoor sights with nothing indoors in between. The fix is to decide on your shelter first: one long breakfast, one or two indoor anchors, and a route short enough that the walk between them is a few streets rather than a trek across town. Done in that order, a wet day in Copenhagen is one of the better ones.

Start with the room rather than the menu. A wet morning is the argument for a café you can sit in for a couple of hours without feeling pushed out, and central Indre By has three we send visitors to. Sonny is on Rådhusstræde, close to Rådhuspladsen Metro, between the old city and the harbour, which makes it the most useful of the three if the day is heading for the museums on Slotsholmen. Atelier September on Gothersgade sits between Nørreport and Kongens Nytorv and is one of the better-known breakfast addresses in the centre. Kalaset is on Vendersgade, a short walk from Nørreport, and is the natural first stop if you are arriving by train or Metro.

If you would rather not commit to one table, Torvehallerne is the obvious wet-weather move. The two glass market halls opened in 2011 on a square that had held an open-air market for centuries, and between them they hold sixty-odd stalls: coffee and pastry counters alongside smoked fish, Danish cheese, bread and lunch counters. The vegetables, flowers and standing tables are outside, so it is the halls themselves that do the work on a grey day. Everyone else has the same idea on a rainy Saturday, mind. Weekday mid-mornings are calm, and the halls stand right next to Nørreport at the top of the centre.

Then pick your indoor anchor, and pick it by where you already are. At the station end of the centre, the Ny Carlsberg Glyptotek stands beside Tivoli: Egyptian, Greek, Etruscan and Roman sculpture on one side, nineteenth-century Danish and French painting on the other, with substantial Rodin and Degas holdings. It was built from a brewer's private collection and opened in 1897, and the part people remember is the winter garden, a glass-domed courtyard of palms, a fountain and marble figures that is warm in any weather.

In the middle of the old city, the National Museum of Denmark is free to enter and large enough to absorb a whole wet morning. The prehistoric rooms are the highlight, with the Sun Chariot, the Egtved Girl, bronze lurs and a remarkable quantity of gold, followed by Viking-age halls and medieval church interiors. Pick two or three sections rather than attempting the lot; two hours is a sensible visit. Further north, Designmuseum Danmark tells the story behind the Danish furniture everyone recognises, with a chair collection running through the whole twentieth century alongside ceramics, textiles, silver and posters. It occupies a converted rococo hospital in Frederiksstaden, nearest the Metro at Marmorkirken, and its displays are thematic rather than exhaustive, which makes it an easy hour and a half rather than a full day.

The National Museum also pairs neatly with a second stop, because it is a couple of minutes from Christiansborg Palace on Slotsholmen, the small island where Bishop Absalon founded a castle in 1167. It is the only building in the world housing all three branches of government, and beneath it you can walk through the excavated ruins of those earliest fortifications. The royal reception rooms and the stables are ticketed, the tower is free to climb, and the courtyards are open to the sky, so on a wet day the ruins are the part to aim for. Slotsholmen has few cafés of its own, which is the argument for eating before you cross one of the short bridges onto it rather than after.

Around Nørreport there is a cluster that suits bad weather almost by accident. The Botanical Garden is free to walk through, and its glasshouses, above all the tall curved-iron Palm House with a spiral staircase running up into the canopy, make it a cold and wet weather option as much as a summer one. The garden belongs to the university and dates from 1874. A few streets away, Rosenborg keeps the Danish crown jewels in its basement treasury and dense royal collections in the rooms above, all of it indoors, with the King's Garden around it for whenever the sky clears. The Round Tower is a near miss worth knowing about: the way up is a broad cobbled ramp of seven and a half turns, built in 1642, and the old library hall halfway up holds changing exhibitions, but the platform at the top is open to the weather. Go for the ramp and the hall, and treat the view as a bonus.

If what you want is to sit out the shower rather than see anything at all, go one neighbourhood out. Baryl Frederiksberg on Holger Danskes Vej is the quieter of its two rooms, serving brunch, coffee and vegetarian and vegan options near Frederiksberg Gardens, and it stays open until four in the afternoon, which on a grey day is the number that matters. In Vesterbro, Sønder Boulevard has Mad & Kaffe at number 68, nearest the Metro at Enghave Plads. Across the lakes in Nørrebro, Café Sebastopol sits on Sankt Hans Torv, a square that is considerably more pleasant seen through a window than stood on in the rain.

Three practical notes. The Metro runs underground across the centre, which makes it the obvious way to move between stops when it is raining, and a grey day is the day to leave the rented bike where it is. Opening times vary more between neighbouring cafés than you would expect, so check the page of the place you have settled on rather than assuming one street keeps one schedule. And a wet Saturday pushes everyone indoors at the same hour, which only sharpens the usual advice: eat earlier than feels natural and the room will still be yours.

Planning around a forecast rather than a single morning? The two-day weekend food itinerary builds both days around where you want to eat rather than what you want to see, which is the easier plan to rearrange when the weather turns. Where to eat breakfast before Tivoli covers the station end of town in more detail, coffee near the Round Tower covers the old university district around Nørreport, and the citywide brunch guide is the place to start if you are still deciding which neighbourhood to give your late morning to. The breakfast, brunch and lunch pages gather the places by meal, for when the plan is simply to eat until it stops.