Die DonauPassau to Vienna.

Linz has the most layered historical identity of any city on the Austrian Danube. Adolf Hitler grew up here (his family moved to Linz when he was nine; he attended school here, developed his artistic ambitions here, and planned to retire here and build the Führermuseum, a monument-complex that would have made Linz the cultural capital of the Nazi empire). After 1945, Linz reinvented itself as a centre of technology and contemporary culture — the Ars Electronica Centre (digital art and technology museum) and the Lentos Museum (Austrian modern and contemporary art on the Danube) are two of the finest museums in Austria. The Hauptplatz is the largest Baroque square in Central Europe.

The Mauthausen concentration camp (1938–1945) was a Class III camp — the highest classification of severity in the Nazi system, designated for "incorrigible political enemies of the Reich." Approximately 190,000 prisoners were registered; at least 90,000 died. The camp was built at a granite quarry: prisoners were forced to carry granite blocks up the 186-step Staircase of Death from the quarry floor. Many were killed by being pushed from the cliff above the quarry (the Parachutists' Wall). The camp buildings, walls, gas chamber and crematorium are largely preserved. The memorial and museum are free. This visit is not optional on a Danube route.

The most spectacularly sited monastery in Central Europe — a Benedictine abbey perched on a rocky promontory 60 metres above the Danube, rebuilt in High Baroque between 1702 and 1736 by Jakob Prandtauer. The building is an expression of absolute Baroque confidence: the twin towers of the church visible for kilometres along the river, the library containing 100,000 volumes including medieval manuscripts (the library setting for Umberto Eco's The Name of the Rose), and the terrace garden suspended over the Danube gorge. The view from the terrace — the river below, the Wachau valley ahead — is the defining approach to the wine valley. The approach by boat from Schönbühel is even better than by car.

Spitz is the most picturesque village in the central Wachau — a small wine town below the Tausendeimerberg (Thousand-Bucket Hill), named for its capacity to yield a thousand buckets of wine in a good vintage year. The ruined castle Hinterhaus stands on the hill above the town; below it, the Spitzer Graben is a side valley planted with apricot orchards that blaze white in April. The Wachau apricot (Wachauer Marille, DAC designation) is the most celebrated stone fruit in Austria — smaller and more intensely flavoured than commercial apricots, made into preserves, Schnapps (Marillengeist), and the Marillenknödel (apricot dumplings) that are the defining dessert of the valley.

The most famous blue tower in Austria — the Augustinian monastery tower of Dürnstein, a brilliant cobalt blue visible from kilometres along the river. But the town's fame rests on its ruined castle above: it was here that Richard I of England (the Lionheart) was imprisoned in 1192–1193 after being captured by Duke Leopold of Austria, returning from the Third Crusade. Richard had insulted Leopold at the siege of Acre; Leopold found his opportunity when the English king passed through Austria in disguise. The ransom (150,000 marks of silver — approximately three times England's annual income) was eventually paid and Richard released. The troubadour Blondel supposedly found him by singing outside the castle walls.

The Wachau is a UNESCO World Heritage landscape partly because of its wine — terraced vineyards on granite and gneiss soil, some of the steepest vine cultivation in Europe, producing two grape varieties: Grüner Veltliner (Austria's flagship white grape — peppery, mineral, age-worthy) and Riesling (here the most complex in Austria, with a mineral depth from the granite that distinguishes it sharply from German Mosel or Alsace Riesling). The Wachau has its own quality classification: Steinfeder (light, up to 11% ABV), Federspiel (medium, 11–12.5%, named after the falconer's lure), and Smaragd (the finest, named after the emerald lizard of the valley, minimum 12.5%). Buy direct at the weingut.

Göttweig Abbey rises on an isolated hill above the Danube plain 15 kilometres east of Krems — a Benedictine monastery begun in the 11th century and rebuilt in Baroque grandeur from 1719 by Johann Lukas von Hildebrandt (the architect of the Belvedere in Vienna). The comparison to the Escorial is apt: the abbey's enormous mass dominates the landscape for kilometres, its twin-towered church visible from the Danube below. The views from the abbey terrace encompass the entire Wachau valley, the Danube plain, and on clear days the Vienna hills to the east. The abbey is still inhabited by Benedictine monks; the wine cellar produces Göttweiger Stiftswein (excellent Grüner Veltliner).

Klosterneuburg Abbey was planned by Emperor Karl VI in the 1720s as an Austrian equivalent of Versailles — a palace-monastery complex that would have been the largest building in the world if completed. Only one-ninth of the planned structure was ever built (four of the planned nine courtyards). What remains is still enormous: the completed section houses the Imperial Apartments (with the Habsburg crown jewels), a Baroque library of extraordinary beauty, and the Augustine Hermits' church with a canopy of carved wood above the high altar. The view over the Danube from the abbey terrace marks the first sight of the Vienna plain as the river emerges from the hills.

The Kunsthistorisches Museum (KHM) holds one of the finest art collections in the world — assembled by the Habsburg emperors over 500 years, in a purpose-built Neo-Renaissance palace on the Ringstraße (1891). The Picture Gallery is the core: Pieter Bruegel the Elder (the world's finest collection — twelve major works), Vermeer's Art of Painting, Cellini's Salt Cellar (the most important Renaissance goldsmith work), Raphael, Titian, Velázquez and Caravaggio. The Egyptian collection and the Greek and Roman antiquities are equally significant. The ceremonial staircase — Klimt's painted lunettes on the ceiling — is itself a major work of art.

The Upper Belvedere palace (1723, by Johann Lukas von Hildebrandt) was the summer residence of Prince Eugene of Savoy — the military genius who saved Vienna from the Ottoman siege and secured the Habsburg empire at the battles of Zenta and Blenheim. The palace now houses the Österreichische Galerie Belvedere, including the world's largest collection of Gustav Klimt paintings. The Kiss (1907–1908) is the defining image of Viennese Art Nouveau — two figures embracing in a field of gold leaf, the man's robe decorated with geometric forms and the woman's with organic flower patterns. The view from the terrace garden over the Vienna city skyline with St Stephan's Cathedral is the finest urban panorama in Vienna.

The Viennese coffee house (Kaffeehaus) is a UNESCO Intangible Cultural Heritage — a specific institution in which a single cup of coffee purchases the right to sit, read, write, think, play cards, and be left alone by the waiter for as long as you choose. The tradition began after the Ottoman siege of 1683 (the retreating Turks left sacks of coffee beans behind); by 1900 Vienna had over 600 coffee houses where every significant intellectual, artist and politician of the city worked. Freud, Karl Kraus, Herzl, Trotsky, Musil, Mahler and Wittgenstein all had regular tables. The Melange (half espresso, half steamed milk, no foam) is the correct order. The waiter will refill the water glass without being asked. You may stay as long as you like.