Vienna: inventing the modern world In Britain, when we think about the dramatic shifts from the Belle Époque to the sudden impact of the modernist movement we tend to look to Paris, where Picasso, Braque, Matisse, Duchamp and Stravinsky were working. But as a new exhibition at the National Gallery in London emphasises, from about 1890 until the end of the First World War, the cultural shifts in Vienna were just as radical, and if anything more broadly based. Among the tight-knit highly educated community of Viennese middle-class intellectuals, artists such as Gustav Klimt and Egon Schiele (whose work is still virtually absent from British museums and galleries), Oskar Kokoschka and the remarkable Richard Gerstl were redefining traditional ideas of painting. The architects Otto Wagner and Adolf Loos were at the forefront of Jugendstil and modernist design, and among the composers in this famously musical city, Mahler was handing the baton to the atonal iconoclasts Schoenberg and Alban Berg. Meanwhile, the playwright Arthur Schnitzler was shocking audiences with his explorations of sexual themes; the young Ludwig Wittgenstein, later to become one of the greatest names of 20th-century philosophy, was battling his inner demons, and Sigmund Freud, in his modest apartment just outside the Ringstrasse, was quietly psychoanalysing anyone who could afford his fees. Freud wasn't always popular with his contemporaries - Mahler's family was furious when he presented a bill for a session held just before the composer's death, and Wittgenstein's sister steered her depressive brother away from treatment because of the rate of suicide among Freud's patients. But he changed for ever the way we think about the human mind. Below is a guide to the city during this cultural and psychological revolution, to help you find the art and architecture that underpinned it. And before you go, pop into the National Gallery to see the exhibition of portraits from the time, and a fascinating overview of the artists and personalities who helped to shape Vienna. Turn-of-the century Vienna The Burgtheater The theatre, opened in 1888, was one of the cultural centres of Viennese society, particularly popular with the emperor, whose mistress, Katharina Schratt, had acted there. The young Klimt was one of the artists responsible for the classical scenes above the grand staircase, and he won royal favour - the emperor's prize - for them. His designs, including his only self-portrait, were discovered in the theatre attic in the 1990s and can be seen on a guided tour. Friday-Sunday, 2pm in German with English summary, €5.50/£4.70, burgtheater.at The Secession Building The Secession was the Viennese art movement of the 1890s - similar to many others around Europe - which was determined to break away from the constrictions of the academic tradition. This ground-breaking Art Nouveau building of 1898, partly paid for by Wittgenstein's father, was built as an exhibition hall for modern art. It still houses Klimt's 110ft Beethoven frieze of 1902 - his interpretation of the Ninth symphony. Admission to the frieze €8.50/£7.20, secession.at Museum of Applied Arts (MAK) Founded in the same spirit as the V&A in London, to promulgate high-quality craft and design, MAK has recently renovated its Art Nouveau rooms, which give an excellent sense of the design trends around the turn of the century and include Klimt's sketches for the wonderful mosaics at the Palais Stoclet in Brussels. €7.90/£6.70, mak.at Leopold Museum Opened in 2001 to house an extraordinarily rich collection of 19th- and 20th-century Viennese art, the Leopold has the most important and largest holding of works by Schiele, perhaps the most powerful and radical of painters working just before the First World War. Admission €12/£10.20, leopoldmuseum.org The Post Office Savings Bank Otto Wagner's minimalist building, designed in 1903, was the first in which aluminium was used as a key part of structure and decoration. The highlight is the banking hall, with its curved glass ceiling and glass-tiled hall. If only all modernist buildings had been built to this standard. Admission free, ottowagner.com Sigmund Freud Museum Following Hitler's Anschluss in 1938, Freud fled his apartment, where he lived for almost 50 years, and where most of his famous psychoanalytical sessions were held, and went to London. It now houses a foundation to further studies on this work. Few of his possessions survive here, but photographs and memorabilia give some sense of what his consulting and waiting rooms were like. Admission €9/£7.70, freud-museum.at The Belvedere The Belvedere Palace - built by Prince Eugene in the early 18th century with a fabulous view over Vienna, is home to the world's largest collection of Klimt paintings, including The Kiss and Judith, as well as paintings by Schiele and Kokoschka. The collection as a whole is enormous, however, and ranges from the Middle Ages to contemporary artists. Admission €12.50/£10.60, belvedere.at Where to eat and drink Palmenhaus The former Imperial palm house, between the Albertina and the Hofburg, is a spectacular Art Nouveau setting. Traditional main courses include Wiener schnitzel (€18.20/£15.50). palmenhaus.at Zum Schwarzen Kameel The Black Camel, which dates from the 1600s and was redesigned in Art Nouveau style in 1901, still has a Belle Époque air about it. The menu is heavily based on meats and stews: saddle of venison in juniper butter is priced at €34/£29; veal goulash at €23/£20. It has an excellent list of Austrian wines. kameel.at Café Museum The café, just by Naschmarkt and the Secession Building, opened in 1899 and quickly became a favourite meeting place for turn-of-the-century artists and intellectuals including Klimt, Schiele, Kokoschka, Otto Wagner and Adolf Loos, who designed the original interior, which was redesigned in 1931. It reopened in 2010 and now serves classic dishes: a Viennese mixed sausage platter with mustard ragout and horseradish will set you back €11.70/£10. cafemuseum.at Loos American Bar Adolf Loos designed this tiny bar, with its angular mahogany ceiling, onyx tiles and marble floor, in 1908 after a stay in the United States - it was Vienna's first American Bar, and a clear rejection of the curves and curlicues of the Jugendstil. It still sells powerful martinis. loosbar.at Read our guide to nightlife in Vienna Nick Trend stayed at the newly restored four-star Harmonie Hotel (harmonie-vienna.at) near Freud's apartment just outside the Ringstrasse. Prices vary, but a double room in late November costs from about €150/£130. Facing the Modern: The Portrait in Vienna 1900 continues at the National Gallery, London, until January 2014; admission £12.50