Copenhagen gets around 170 days of rain a year, which means if you only date in good weather, you don't date much. Locals have figured this out. The good news is that the indoor culture here is genuinely strong, partly because of hygge, partly because the alternative is standing in a drizzle on a bike. Here's how to plan around the weather.
The long museum afternoon
The Glyptotek on Dantes Plads is the best rainy-day museum in the city for a date, and I'll fight anyone who picks the National Gallery instead. The winter garden in the middle, with its palm trees and fountain and cafe tables, is essentially a free indoor park. You can wander the Roman busts and the Rodin collection for an hour, then sit in the conservatory for another hour and order coffee and cake. The ticket is around 125 kroner and is free on Tuesdays for the permanent collection (check the website, the rules shift).
If you've already done the Glyptotek, the Designmuseum on Bredgade is the second pick. The chair gallery alone takes thirty minutes if you actually stop and read, and the cafe in the courtyard is a good rainy-day lunch.
Bathhouses and the wet kind of indoor
If it's already pouring, lean into it. SØS Sauna in the harbor or Sauna Lab on Refshaleøen both run heated sessions where the rain on the wood roof is part of the atmosphere. For a more elaborate version, Sport & Spa in Hellerup or the Frihavnstårnet sauna gives you a proper afternoon of heat and cold. None of these are cheap (figure 200 to 350 kroner per person) but they turn bad weather into the entire point of the date.
Københavns Badehotel and the Kastrup Søbad sea bath are also options if you're committed, but those are more polar-plunge than romantic.
The long lunch
Copenhagen does the slow weekend lunch better than almost any city its size. Apollo Kantine in the Charlottenborg courtyard is my pick when the weather is bad. The room is bright, the menu is short, and you can sit for two hours with a bottle of wine and not feel rushed. Hart Bageri on Gammel Kongevej, the Noma-affiliated bakery, is the other move for a daytime rainy date. Order a sandwich and a pastry, sit at the counter, watch the rain hit the windows.
For a longer commitment, Pompette on Møllegade does a three-hour lunch on weekends that turns into early dinner without anyone noticing. The room is small, the lighting is forgiving, and the wine list is the kind that makes you want to stay.
Cinemas worth a date
Grand Teatret on Mikkel Bryggers Gade is the proper art-house cinema in the city center, and the bar in the lobby is a real bar, not a popcorn counter. You can get there an hour early, drink a glass of wine, see a Danish film with English subtitles, and have something to talk about afterward. Empire Bio in Nørrebro and Vester Vov Vov in Vesterbro both have similar formats. Tickets are around 100 kroner.
Skip the multiplexes downtown unless you specifically want a Marvel movie, in which case more power to you.
Bookshops and the slow browse
A rainy afternoon in a bookshop is underrated as a date format. Thiemers Magasin on Tullinsgade in Vesterbro is the best small bookshop in the city for English-language fiction. Politikens Boghal on Rådhuspladsen is the bigger version, with a cafe upstairs. Atlas Books on Larsbjørnsstræde does art books and the kind of weird zines you didn't know you wanted. Pick something for each other. The book itself doesn't matter, the picking does.
Tivoli in winter
If it's raining and it's December, Tivoli's Christmas market is a defensible date, despite the tourist load. The covered halls, the fire pits, the gløgg stands. It's actually better in light rain than in clear cold, because the lights blur and the crowds thin. A regular admission is around 155 kroner, and you don't need to buy ride passes unless you're committed. Two hours is the right amount of time. Eat dinner somewhere else.
A practical note
Dress for the rain and stop checking the forecast. Danes have a phrase, "there's no bad weather, only bad clothes," which is annoying when you're cold but mostly true. A good rain jacket and waterproof boots will get you through any of these dates without complaint, and being the person who showed up prepared is its own small flex.