We set a target of pounds 150 to cover everything, checked into a pounds 10-a-night hostel and set about seeing the sights with a three-day travelcard, costing 130 Austrian Schillings (pounds 8.50). This allows unlimited rides on the trams, buses, U-bahns and rapid transit Schnelltrains anywhere within 'zone one'. But this is no stingy London-style zone one; passengers can travel for at least an hour in any direction from the centre.
The city's best-known sights are in and around the Ring, a wide pentagon-shaped boulevard skirting the centre. A good journey to start with is 'tram one' which circles it endlessly - rather like an above-ground version of the Circle Line. We sat back and got our bearings as we trundled past the Austrian Parliament, the Opera House and the Danube Canal. 'Tram two' does the same 30-minute journey in the other direction.
Another good idea is to take the U1 to the Prater Park, ride on the giant ferris wheel for pounds 2, then stroll along the Danube Canal to any U4 tube station on its banks. The U-bahn is cleaner and less congested than London's Tube, trains are less claustrophobic and there stations have shops, cafes and lavatories.
Prices in Vienna, however, are even higher than London, so keeping your spending under pounds 150 means making sacrifices. You could linger over a coffee (pounds 2 minimum, and much more with cakes) in the Cafe Central where Trotsky was a customer. Cheapskates should just hang around in the foyer, check their watches, admire the recently refurbished interior, and pay nothing.
Everywhere teenagers in ludicrous 18th-century costumes give out flyers advertising classical music concerts; a nice idea, but pricey at about pounds 21. Cost-wise, this is the equivalent of three nights exploring Viennese bierkellers, dark, converted wine cellars with low-arched brick ceilings. Our favourite was one of the city's oldest, the Zwolfapostelkeller (Twelve Apostles) in Sonnenfelsgasse. It dates back to the 16th century; the vaults are popular with younger drinkers, while a more middle-aged crowd sits upstairs. Note the intricate clock decorated with figures of the Apostles armed with hammers, used to strike each hour.
A strangely reassuring place for the impecunious is Cafe Hawelka on Dorotheergasse, which has free newspapers. It was once a haunt of artists, and those unable to meet their bills handed over paintings instead which are still displayed. Waiters fetch your drinks but the place exudes informality and friendliness - an atmosphere you also get at Die Tunnel in Florianigasse, which attracts younger drinkers and students.
In most bierkellers, half a litre of beer will cost you pounds 2; some, as we found charge a lot more. My friend has a weakness for Guinness and we found ourselves paying pounds 4 a pint at one of the centre's 'Irish' bars. That kind of mistake hurts when you are lunching on supermarket bread and cheese. Try eating lunch in the Belvedere Imperial Gardens or at the superb Schonbrunn palace, both great settings which do not have admission charges. Get the tram or U-bahn back to the centre to the stunning decoration of the Karlskirche church, and on to see Gustav Klimt's Beethoven frieze in the art-nouveau Secession building's basement. Admission is pounds 2 but worth it: the frieze depicts female figures surrounding the composer.
The Modern Art Museum at the Palais Luxembourg is 10 minutes away by tube: entry is pounds 2.70 for adults (pounds 1.80 if you can pass for a student). There are plenty of big names, such as Max Ernst, Joan Mir and Rene Magritte, although the works that stand out come from the Italian Futurist Giacomo Balla and the Romanian sculptor Constantin Brancusi.
Most of the composers who made Vienna their home are buried in a small cluster in the central cemetery (Zentralfriedhof), a 45-minute ride through the south-eastern suburbs. A short walk brings you to the last resting places of Beethoven, Schubert, Brahms and Strauss. Mozart takes pride of place but, as he was originally buried as a pauper in an unmarked plot in an obscure graveyard, this is a retrospective gesture.
Here, too, the classic final shot of Carol Reed's The Third Man was filmed along a wide path. You can even go on Third Man city tours: these cost about pounds 8.50 and reveal some of the film's secrets. For a DIY version, however, head for Josefsplatz to see the scene of Harry Lime's 'accident', the Prater Park for the ferris wheel sequence, and Albertinaplatz for the Mozart Cafe.
So much city travelling is exhausting, and staying in a hostel may not be a brilliant idea. Certainly, it's cheap - half the price of a bed and breakfast - and good value. You get a bed, a locker, use of a shower and kitchens and a continental breakfast. But, with up to eight in a room, you tend to be woken regularly between 11pm and 1am as people get back from bars.
By day three my friend and I were competing to see who could cover most ground, and I headed off for a morning's excursion by tram and bus to Kahlenberg, a village nestling in the Vienna woods. From here you get a panoramic view of the city, the Danube and surrounding hills.
I had become absorbed in routes and schedules and as the bus took tight bends to the crest of the hill, sharp pains shot across my stomach. I willingly paid for a meal at a pizzeria near Beethoven's former home in Heiligenstadt.
In the end, we stepped off Tram D at Sudbahnhof for our train back to Prague with pounds 10 to spare. . .and strange memories of the underground. Each stop is announced by the same man on tape: I had made so many rides, this had become like a mantra, and his measured mechanical tones still creep eerily into my dreams. . .
Visitor's fact file
British Airways (0345 222111) has a pounds 199 fare from Heathrow; cheaper tickets should be available through discount agencies.
Vince Hunt paid pounds 10 a night at the Hostal Zohrer,
Skodagasse 26 (010 431 406 0730).
Austrian National Tourist Office, 30 St George Street, London W1 (071-629 0461).
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