Ronald Reagan was a man who knew the diplomatic form. He also had a showman’s ear for a tune. So when, at an official dinner, the marine band slipped into Edelweiss, he stopped mid-anecdote, rose to his feet, placed a reverential hand over his heart and stared into the blank mid-distance out of respect for the Austrian national anthem.

This possibly calumnious story pulls out a truth not so much about American presidents but about Austria. It is a greatly misunderstood and trivialised country.

Being justly and stiffly proud and protective of their extraordinary musical heritage (Berg, Bruckner, Haydn, Mahler, Mozart, Schoenberg, Schubert, two Strausses and Webern are just the ones you can hum from memory), Austrians fail to see the humour in the fact that around the world their theme tune is a musical written by two New York Jews, and that those of us who wouldn’t know whether to blow, swallow or applaud Die Zauberflöte all know that doorbells and sleigh bells and schnitzel with noodles are a few of Austria’s favourite things.

And Vienna – where Mozart lived and Mahler directed the opera – has a signature tune from a British film played on a Russian stringed washboard (The Third Man). Vienna is a city that’s made a virtue out of rising above the slings and arrows and mockery of cruel fortune with a pose of glacial disdain and the sigh of the socially martyred. It all clings to a scuffed dignity. Despite all their illustrious ancestors, still the most famous Austrian is Christopher Plummer.

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There’s a funny thing about Vienna. You don’t notice immediately; it creeps up on you and hits you between the eyes. The doors all open the wrong way. The Viennese just decided contrarily to have doors push into the street rather than pull into the hall.

Perhaps it’s a small act of rebellion against being mistaken for Germans. So you spend a lot of time drücken when you should be ziehen. For some time I’ve had this feeling about Vienna – a Fledermaus squeak of synchronicity. Its name came up once too often; I had a sense that it’s a coming destination. It’s a city with so much behind and so much front that it’s about to happen.

It was suggested that I took my newish twins. So mother, babies, nanny and Tom the photographer and I all went to Vienna for a winter weekend. Weekend breaks have become a feature of the northern European life that cuts leisure time like cucumber sandwiches into little triangles.

We need the crusts off our holidays, and since the opening of the land beyond the Danube and the euro, the cities of far-flung Europe from Barcelona to Riga have been overrun by berserk, Hunnish hordes of gel-haired drunks in matching T-shirts and squadrons of feral bridesmaids with matching brazilians.

The Continent is where we go to act out and up. But not Vienna. This is no place to let your hair down or get your buttocks out. This is grown-up Europe, a city for adults. You don’t act your age here, you act a couple of decades older.

The waiter looked at the double buggy the way a french-polisher might regard a lawnmower on a dining table, and suggested ever so politely that he could put it somewhere else. “It’s not in the way,” I said, “not blocking a corridor or fire exit.” “No, but it could go out of the way.”

I realised his objection in this gingerbread-and-crystal coffee and cake emporium was aesthetic rather than practical. “But,” I added, “it’s got a pair of children in it.” “Yes,” he said uncertainly, realising that this probably brought the conversation to a close, but not quite understanding why.

Vienna isn’t child-friendly. But it’s not just children. It isn’t anybody-friendly. Frail, lovable humanity isn’t Vienna’s bag. Watching the Viennese go about their daily business, you see they’re not people people, not particularly warm to each other. What they are instead is polite, with immensely good, lightly starched manners, and this is such a joy after coming from a social climate of enforced, instant mateyness and small talk. The thoughtful formality of etiquette is a blessed relief. You forget what a strain friendliness is until you don’t have to do it.

Viennese restaurants don’t have dress codes – they don’t need to, because Vienna has one. Often rather eccentric, there is a lot of rural, musical hunting gear worn by both sexes. Furry pig’s arse on green felt hats, double rows of horn buttons, military-fetish goat skin and things made out of carved antlers.

I found an old jewellery shop that specialises in setting teeth in silver, which is both compulsively fascinating and perineum-clenchingly shuddery – and which is true of so much of Vienna. Though I’d been warned about the elaborate verbosity of the architecture, nothing quite prepared me for the incoherent cacophony made up of marble expletives and hysterical, psychotic plaster-laughter. The buildings silently bellow and leer at you. For a start, it’s their sheer scale.

Utterly unhuman, they all start with the assumption that everything needs to be XXL, the size of a 17-platform railway station built in the municipal classical style, with a Babel of pedestals, columns, pilasters and assorted architraves, then decorated with a giant confectioner’s piping bag with figures and images whose associations would defy the imagination of a priapic, visionary hermit.

Naked angels riot with double-headed eagles and fight the fish-people, naked bodybuilders club goatmen, lions are strangled by alligators, ethereal brass bands and Valkyrie cheerleaders helter-skelter across the roofs. A rampant cornucopia of bodacious, perky, muscle-bound, up-for-it nudity.

On the street, the Viennese are the most conservatively buttoned-up, primly polished people in Europe. Just above their heads there are godly roastings and snuff orgies like baroque cartoon thought bubbles. It’s no coincidence that Freud came up with the id, the ego and the subconscious in Vienna – it’s no coincidence because Freud said there are no coincidences, but it does make you wonder what psychiatry would have been like if he’d lived in Belfast or Belgium.

Vienna looks like a city that is always trying to prove something to itself. It lives on civic steroids. Other places had bigger empires, more money, more successful armies, but nowhere ever proclaimed itself to itself with such grandiose ardour. But the most striking and impressive object in Vienna is the simplest and the most modern, and the one I expect the Viennese resent and dislike the most: it’s Rachel Whiteread’s mordant stone library, which is the memorial to Austria’s lost Jews.

Vienna was once a Roman cavalry outpost on the Danube, guarding against the incursion of the Huns. Austria means “eastern realm”. It was civilisation’s East End, on the edge of our world. Through decline and decadence it came to be the capital of the Holy Roman Empire, with all the vainglory of snobbery that entailed. Most crucially, the siege of Vienna was the turning point in the western march of the Ottomans.

The timely intervention of Polish cavalry raised the siege, and it became one of the top three events in western history – indeed, it allowed western history to get on. And it gave us the croissant. It is another stoically borne calamity for the Viennese that these are thought to be French when they’re Austrian, as are bagels, though strangely, Wiener schnitzel may actually be Italian – a Milanese with the bone cut off, bought back by Field Marshal Radetzky, who had the musical march.

Vienna has always been on Europe’s turbulent edge, the front line against Ottomans, Huns and communists. It was a fulcrum, and for all its whiskery probity and pursed-lipped snobbery, it has produced more staggeringly impressive first-flush culture than any other European city – not just music but science, philosophy and art.

The secessionists Klimt and Schiele, the writers Joseph Roth, Rilke, Schnitzler (who was in prison for the uncompromising sexual play La Ronde), and that most Viennese of socialists and utopian essayists, Leopold von Sacher-Masoch, who wrote Venus in Furs and painfully gave his name to the world as masochism. Sacher-Masoch: half spanking, half cake – so very Viennese.

Although the buildings are monumental, the city is very human-sized. You can walk everywhere. The streets in winter are effulgent with the thick smells of gingerbread and gluhwein. The shop windows grin and shimmer with pastries and cakes and chocolates and carmine G-strings. There is a laughable number of lingerie shops with mannequins quite as explicit as the baroque decoration. All Vienna’s interiors are terribly overheated, so you see lots of women wearing vast fur coats in the street with plainly very little on underneath.

Despite all its über-civilisation, Vienna’s principal gift to humanity is the cafe. Thanks to the coffee left behind by the Ottomans and the chocolate donated by the Spanish branch of the Hapsburgs, Vienna invented the most perfectly civilised venue in all human culture.

Cafes have spread to every corner of the world: from the high Himalayas to the oases of the Sahara you can sit in a cafe. They are Vienna’s gift to all of us. Properly egalitarian, they belong to everyone – you can read a paper, talk bollocks, write a book about alienation or discover an Oedipus complex.

Cafes aren’t just the transcendent examples of civilisation, they are the crucibles of culture: more great thoughts have been had in cafes than in all the world’s universities, and Vienna has the finest and the best.

Demel is perhaps the most famous; cake-makers who fought a ridiculous, Roald-Dahlish legal battle against the Sacher hotel about who had the original secret recipe for Sachertorte – did the apricot jam go under the icing or in the middle? The cafe has waitresses in old-fashioned black-and-white uniforms, and glass cases of cakes and pastries that look like jewels.

There are jugs of the finest hot chocolate and alpine ranges of whipped cream. It all exudes that slightly spooky feeling of a cautionary fairy tale. You can watch the patissieres wearing floppy chef hats that no other cook has worn for 80 years, hand-make iced cakes in the shape of naked women – of course – and animals.

I watched a girl spend 10 minutes getting a white-spotted sugar pig just so. Vienna is one of the last places in Europe where the making of things that are important – like spotted iced pigs – is done to a nostalgic tradition, not a commercial equation.

At the end of the war, the Germans looked at their shattered country and their flattened industry and made the decision to take the American cash and build a whole new economic miracle. It seems that confronted with the same catastrophe, the Austrians chose instead to rebuild the past, to wrap themselves in the comfort and the glory, the whipped cream and good manners, and the understanding that the best Austria could ever hope for was already behind them and the closer they kept to their history, the better.

Vienna is a city without a future, and that’s the way they like it. It’s also the way I like it; a marvellous, echoing place of ghosts and white horses and music. And if you come away with anything, it should be the fact that Christopher Plummer isn’t now the most famous Austrian. Arnold Schwarzenegger is.

How to get there

Seasons in Style offers three nights at the Hotel Imperial from £820 per person, based on two sharing, inc. flights. Tel: 01244 202 000; www.seasonsinstyle.com

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