I lived in Vienna once, when I was an astrophysicist: an apartment between Grunangergasse and Blutgasse; my coffee at Diglas; my dinner customarily at Oswald & Kalb or Da Capo; the 11 o'clock Mass at the Stephansdom, in the Unterkirche – so much more austere and elegant than the 10.15 musical jamboree for tourists. It was a city turned towards its past, a living chiaroscuro, stark sudden light on wet cobbled streets, a city seen through a haze of tobacco-smoke, a city which no longer exists, and never did exist, nor was I ever an astrophysicist. I never lived in Vienna, not once.

I just told people I did. It was at a party. I was very drunk; to deflect the attentions of a woman – gorgeous, but my heart was elsewhere – I invented the Vienna astrophysicist story to explain why I had to leave. Two hours later I was still talking about my life there, to people I had known for years who knew perfectly well I was making it up; but they were very kind. Very understanding. I expect they all had another self who was an astrophysicist in Vienna, too.

And zither music accompanied me all the way home to Paddington.

Where the astrophysical me had lived was, of course, not Vienna, the capital of the sometime Austro-Hungarian Empire, musical centre of the world, birthplace of psychoanalysis, but Graham Greene and Carol Reed's imaginary city of The Third Man, the 1949 masterpiece of municipal noir. Greene and Reed defined or created an entire city, and now that overlay upon the geographical Vienna can never be unseen, nor can you unhear Anton Karas's chillingly jaunty zither music, forget the sewers running beneath the streets, walk around on a sunny day without searching for the impossibly dramatically-lit night alleys glistening with rain. If ever there was a city defined by one work of art, it is Vienna. But The Third Man has arguably also utterly masked it. No amount of schlagobers nor any quantity of Christmas punch can drive away the rubble, the shadows and the hard, dutched camera-angles from the mind's eye.

There is, of course, a Third Man industry. Health & Safety put a manhole on the famous tour of the sewers (actually part of the Wienkanal, carrying the Vienna River flows into the Danube) through which Harry Lime flees; rats and risk of flooding, they said, though last summer an enterprising operator restarted them with the aid of an accompanying bagpiper: the music drives the rats away. There's also the Vienna Underground Club, which holds regular events like subterranean dinners below the streets. You can take a tour of the locations in the film: Dr Winkel's house off the Burggasse, Harry Lime's apartment at Josefsplatz 5, the – probable – entrance to the sewers in Karlsplatz, the Café Mozart, moved from its real location next to the Hotel Sacher (of torte fame) up to the Neuer Markt... even the sewer-grating by the Minoriten-Kirche through which Harry Lime's fingers made their final clutch at freedom; though it's not the same grating and in any case they weren't Harry Lime's fingers, or even Orson Welles' (who hated Vienna) but Carol Reed's.

And there's the nub of it. The platonic Vienna, the ideal death-haunted chiaroscuro of night and rainy streets, of lights flaring in the darkness and gunshots heard but unseen, of the deserted Prater funfair... none of it was ever real. Reed and Greene's Vienna depended too much on the landscape of Greeneland, realised and expanded by cinematographer Robert Krasker's extraordinary Germanic expressionism of lines and planes, impossible contrast and tense orthogaphics. To look for it in reality is to be confounded.

What is there, though, is an echo (etiolated by modernity, by the bossy street furniture of the EU and its hatred of risk, dirt and shadow) of the Wien that the post-war multipartite administration temporarily interrupted. It's not so much that the Vienna of Tales of Hoffman or even Strauss's waltz-madness is erupting from every street-corner; more that the city still has a kind of gemutlich dignity and courtesy which has vanished from most modern capitals. Men wear hats and raise them when – "Gruss Gott" – they greet a lady. The coffee-house is still an institution; I like Hawelka in Dorotheergasse, Diglas behind the Stephansdom cathedral, and the Kleines Café in Franziskanerplatz, but everyone has their own favourites, the key thing being that your coffee buys you a prolonged right of sojourn. Think of McDonald's; the Viennese Kaffeehaus is the opposite. (But think of Starbucks' ludicrous ordering-system: the Viennese is infinitely more complex. Ask for "coffee" and you won't get anything. What you need is an Einspanner or a Fiaker, a Verlangeterer or maybe a Turkischer or a Cappuccino, which isn't a cappuccino because it's made with whipped cream and if you want a cappuccino ask for a Mélange, though frankly what you want is a Fiaker: shot of rum, whipped cream. It's snowing outside, for heaven's sake. If it's not snowing, you'll have a Mazagran, which is essentially a colder, sweeter Fiaker. Clear? Good.)

Vienna is a profoundly Roman Catholic city. Sundays at the Stephansdom – rebuilt after its bombing in the Second World War; still in ruins in The Third Man – is a beauty parade of handsome men in Loden coats (the word means "rich banker" in Viennese German) or the traditional Trachten with silver buttons, their glossy wives in furs and their adorably Austrian children. "Before the Anschluss," an artistocratic friend told me, "my uncle the Cardinal used to get his scarlet silk underwear made at Knize," and the shop, Vienna's finest tailor, is still there in the Graben; the faint elegant leather-and-tobacco scent whose sillage remains after the families have gone into Mass is François Coty's Knize Ten. You might catch it in one of the smaller dining rooms at the 15th-century Griechenbeisl, where a 17th-century musician called Augustin composed and sang a wry song about the poor business caused by the plague of 1679: "Ach der liebe Augustin", or at the Konig von Ungarn, which has been a hotel without interruption for over 400 years.

And yet all the elegance which Vienna has recaptured comes at a price. The Third Man identified a particular instance of a more universal fact: that the city seems to lie along a fault-line in European history, and that what Greene called its "bogus easy charm" is built on a less easy or charming foundation. The fate of Vienna's Jews is well-enough known. Rachel Whiteread's memorial house is more chilling than can be imagined. And while the order and civility of the city and its people are beguiling, I must remind myself that I am being beguiled as a middle-class, educated white man, and try not to look too closely at why I find Vienna so oddly comforting.

The tension in her fault-lines might explain the city's preoccupation with death and with the "schone Leiche" or, in the Viennese dialect "a scheene Leich" – literally, a "beautiful corpse", a good funeral. "Leich": a word ideally-suited to the nasal Viennese accent, and appropriate, too, that Greene's screenplay begins and ends in the great cemetery of the Zentralfriedhof in the shadow of the Karl-Lueger-Gedachtniskirche. A good place to begin Vienna-in-a-day, perhaps; then to the Prater gardens for a ride on Walter Basset's Riesenrad, the 213ft big wheel, where Orson Welles improvised the cuckoo-clock speech which was one of the two things Graham Greene hated about the film (the other thing was the zither music, which he said was simply dreadful and ruined the mood). Then on to Freud's house, where he formulated the Death Instinct; the Josephinum museum to see the 18th-century wax anatomies used by medical students; to the Staadtsoper, preferably Rosenkavalier (or, in the summer, a concert at the Karlskirche and never mind which, because the programme is always the same: Mozart's Requiem, composed at Rauhensteingasse 8 (handy for a Turkischer at Gerstner or dinner at Kuckuck); then finish with death-songs at a traditional Heuriger wine-tavern. Don't expect zither music, though; and do remember the cuckoo-clock.

Vienna: art, shangri-la & the waltz

* The opening of the Shangri-La this spring will bring Eastern charm to Vienna's 19th-century Ring Strasse. Set in the former Erste Bank building, the hotel occupies an entire city block and has a spa plus treatments based on Chinese traditions; shangri-la.com/en.

* Spend a day exploring the Museums Quartier. This strikingly designed museum complex is set in the former imperial stables. The site celebrates its 10th anniversary this year with an enormous programme of stellar shows; mqw.at.

* Each year, more than 300 balls take place in Vienna. The city of waltzes celebrates carnival from January until early March at venues across the city. Highlights include the Coffee-house Owners' Ball (25 February) or the sweetest and perhaps most informal, the Bonbon Ball (4 March); wien.info/en/.

* Vienna's 19th-century Central Cemetery is the final home for such musical luminaries as Beethoven, Brahms and... Austrian pop sensation, Falco. With over 300,000 graves, Europe's second-largest cemetary is easy to get lost in. But you can now explore this tranquil spot with an English language audio tour; vienna.info/en.

* Visit the former residence of Austrian painter and architect Friedensreich Hundertwasser. With undulating contours and psychedelic colours, this huge apartment block has become a pilgrimage spot for art and photography lovers; hundertwasserhaus.com.