The weekend city break from hell goes like this. It rains. You’re not exactly lost but where you want to be is elusive. You bicker incessantly with the poor soul you dragged away with you. You left home in the wrong shoes, and they’ve got a hole.

Every path leads to a dual carriageway with a bus lane but there are no bus stops. You and your companion take turns to be too stubborn to ask the way and too mean to take a taxi. You argue about whether you should go and argue in a cafe, but the argument takes you past all the cafes. You walk some more, it rains some more, you argue some more.

Thanks to all those “outer Mongolia in 48 hours” columns in the travel sections, the misery is enhanced by the knowledge that you are six hours down and have clocked up no acutely pleasurable experiences.

Such negativity gets you nowhere in Copenhagen, where even the airport is bright, positive, efficient and well designed. Opposite the airport bus stop there’s a tidy building site where everyone wears matching sweatshirts. No builder’s bum here. Wild flowers grow along the route into the city; the Danes use lead-free petrol, and it works.

On the way to our hotel we peered into the waterlogged Tivoli amusement park. In the downpour, Tivoli looked like the British Bank Holiday experience writ large, but the hot dogs smelled better and the rainwear was classier. The pleasure-seekers seemed unperturbed at having to endure an English April in August. The posters said “God Sommer”, and a God Sommer they were going to have. Flotillas of cyclists whizzed by - the cycle lanes go everywhere - a few of them doing high-spirited wheelies. There were flyers for open-air cinema, theatre and concert seasons scattered around town and strawberry tarts in all the bakery windows.

I was instantly suspicious of the veneer of rational well-being and did my best to tap a seam of chaos beneath. On being told that we couldn’t have our hotel room for three hours, I burst into tears. (I had been up since 4am and have clearly gone soft in the 10 years since I backpacked in the Andes.) The receptionist, appalled at this untidy show of feeling, did the only sensible thing and ignored me until I slunk away.

As one downpour merged into another, we trudged to Christianshavn and our first stop, the Filmhuset (Museum of Danish Film). Christianshavn is a formerly working-class area now being gentrified. The Film-huset was not only closed, but well on the way to becoming another tidy building site - it’s been sold to developers.

Round the corner was Vor Freslers Kirche with the helter-skelter staircase on the outside of its spire, but there was no chance of seeing the view from the top because the 400 steps were treacherous in the rain. Cue for more tears - but the sun came out (briefly) and you could see enough gilded roofs to understand what Hans Christian Andersen was excited about.

We reminded ourselves that we were lucky to be here. I put the tissues away and enjoyed strolling along the Wilders Canal past barges banked with geraniums. We took the Knippels bridge back to the city centre and steamed (literally) across town to the Friheds-museet (Museum of the Danish Resistance Movement) on the Esplanade. We got there 20 minutes before closing time, and the displays about Denmark’s stint as an occupied nation and its history of sabotage and non-co-operation and the fate of its refugees merit at least an afternoon. Recovery was in order. We found a cafe, and I threw my shoes in the bin and bought some fetching orange wellies.

Modern Copenhagen’s strengths are its cafe society and its investment in everyday beauty which means functional objects look wonderful and florists and hairdressers thrive. In the grungiest rock venue we could find, there were flowers and candles on the tables and clean-cut Danes were playing REM covers.

Survival as a visitor is straightforward once you have shed the negativity. You don’t have to buy bus tickets before you get on the bus. You pay before you eat; you don’t have to tip. Everyone is friendly and helpful - bus drivers are happy to let a queue form while they explain the route.

When we finally collapsed into our hotel room, we found that it too was collapsible. The bed pulled out of the wall and the chairs were self-assembly. Either it was an ingenious designer solution to the shortage of cheap accommodation above hostel level, or we had strayed into Sweden (IKEA land), which would explain why we had failed to spot the Little Mermaid. She gets littler by the day as vandals keep removing her limbs, so I don’t entirely blame myself.

What else didn’t we do? We missed the Carlsberg modern art gallery with its sculpture conservatory. We didn’t hire bikes (the best way to get around) but we enjoyed talking about it. We didn’t phone Wonderful Copenhagen, the tourist information line which could have pointed us to the film museum.

What we did was spend so long at the wonderful Louisiana collection of modern art in Humelbaek (an attractive coastal commuter village 40 minutes by train from Copenhagen) that we committed the ultimate tourist crime and didn’t get to Helsingor“Elsinore” to see Kronborg Slot - “Hamlet’s Castle”. Anyway, I have my doubts about Hamlet’s Danish lineage. He wasn’t positive enough and he never mentioned getting his hair cut.

Geraldine Brennan flew to Copenhagen with Virgin Express, which offers return flights for pound;101 via Brussels from London Gatwick or Heathrow. Bookings on 0171 744 0004. Go, the British Airways budget airline, offers a pound;100 return fare direct from London Stansted. Bookings on 08456 054321. These fares are subject to availability and other conditions