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.