Get ready for a rush on sales of gold-leaf paint. Gustav Klimt: Painting, Design and Modern Life in Vienna 1900, which has just opened at Tate Liverpool, has a fabulous lineup of Klimt's paintings, alongside furniture and artefacts by his contemporaries. It also offers a fascinating glimpse into life in fin de siècle Vienna. But for the authentic Gustav Klimt experience, nothing beats a visit to the city itself.
Klimt's best-known paintings are the lavishly decorated pieces from his "golden period" – sumptuous mosaic-like creations, with jewelled rectangles and exquisite discs of gold and silver spilling down the pictures like showers of coins. Fittingly, a tour of the galleries of Vienna to look at his works in their home setting offers plenty of glamour and glitz. The most famous paintings, including The Kiss, are housed in the Baroque splendour of the Upper Belvedere Palace, one of two magnificent mansions divided by a ravishing landscaped slope of formal gardens. Another fine display of Klimt paintings can be found in the limestone cube of the Leopold Museum, which opened in 2001 as part of the city's Museumsquartier.
However, there's a lot more to Klimt's Vienna than palaces and ritzy galleries. Though only one of the three studios where he worked is still standing, and the apartment block at 36 Westbahnstrasse where he lived for most of his life offers nothing more interesting than a plaque on the wall, you can easily retrace Klimt's footsteps to the artist's other favourite haunts. Visit the eastern edge of the lovely park at Schloss Schönbrunn, for example, where he ate the same huge breakfast every morning (with a side order of whipped cream) within sight of the city zoo. Or stretch out in the Prater gardens – home to Vienna's giant Ferris Wheel since 1897. In 1902, Klimt entertained the sculptor Rodin in these gardens, surrounded by the neighbourhood's most beautiful nymphets. (Rodin obviously thought he'd died and gone to heaven. "This garden, these women, this music," he rhapsodised. "What is the reason for it all?")
Bear in mind as well that a number of Klimt's works were created on site – including the magnificent Beethoven Frieze, a replica of which is now on display at Liverpool. You can have the thrill of imagining yourself standing exactly where the artist himself must have painted, resplendent in his floor-length indigo smock (allegedly with nothing underneath).
My own pilgrimage in the great man's footsteps began, simply enough, on tram No 1. It follows the 6km course of the Ringstrasse, the most magnificent of Vienna's thoroughfares and a piece of history that Klimt himself played a part in creating. Known to locals simply as "Ring", the vast, tree-lined avenue was a showcase for imperial wealth. It encircles the city centre like a horseshoe and boasts an awesome parade of grand municipal edifices. Between 1860 and 1890, newly commissioned buildings included parliament, the city hall, the university, the museums of natural history and fine art, a theatre and the state opera house – all ostentatiously neo-classical in style.
Trams 1 and 2 circle the Ringstrasse in opposite directions, giving (quite literally) ringside views of the whole over-the-top extravaganza. To inspect Klimt's contribution, hop off at the Kunsthistorisches Museum and visit the first-floor balcony, where the young Gustav and his brother Ernst completed a series of rather florid murals. Then stroll westwards to the Burgtheater, where they painted some altogether more imaginative ceiling frescoes. Guided tours of the frescoes (in German) run every afternoon for €5.50 (£4.60).
The most impressive of Klimt's site-specific creations, the Beethoven Frieze, was painted some 15 years later than the Ringstrasse works, for display in the iconic "Secession" building. The Secession movement was founded in 1897, with the 35-year-old Klimt as its first president. Its artists developed a distinctive Viennese version of Art Nouveau that became known as Jugendstil. Their flagship building is extraordinary – a windowless white block sparsely decorated with golden relief work and topped by a gilded dome of entwined laurel leaves.
The modernity of the design provoked uproar at the gallery's opening in November 1898, with the gleaming foliage of its cupola quickly earning it the "Golden Cabbage" nickname that it retains – now affectionately – to this day. The 34m-long Beethoven Frieze was constructed here in 1902, and triumphantly restored to its original setting in 1984. If there's a single "must-see" in Klimt's Vienna, then this it.
The final tram ride on my Klimt trail was less spectacular, but in its own way just as thought-provoking. The elegant south-western suburb of Hietzing is Klimt's burial place. But it was also his last home in the city, and the location, from 1912 until his death in 1918, of his final studio.
Tram 58 runs from Hietzing Hauptstrasse to Unter St Veit. Disembarking at an unprepossessing Chinese restaurant at Feldmuehlgasse, I headed for 15a. In Klimt's time, the building was a one-storey Biedermeier house, in a large garden of flowers and fruit trees that the artist tended himself. Later, it was all but obliterated when a neo-Baroque villa was built up around it. Now, acquired by the government but awaiting restoration to re-expose the studio within, the mansion languishes as poignantly as Sleeping Beauty's palace in its tangled wood of thorns. Wouldn't it be wonderful if the renewed interest in Klimt's work could lead to a reawakening?
Belvedere Palace (00 43 1 79 5570; www.belvedere.at). Schloss Schönbrunn (00 43 1 811 13239; www.schoenbrunn.at). Kunsthistorisches Museum (00 43 1 525 240; www.khm.at). Vienna Tourism (00 43 1 24 555; www.wien.info). 'Gustav Klimt: Painting, Design and Modern Life in Vienna 1900' is at Tate Liverpool until 31 August (0845 600 1354; www.tate.org.uk)