A prince-archbishop with a wicked sense of humour, Markus Sittikus, built Schloss Hellbrunn in the early 17th century as a summer palace and an escape from his functions at the Residenz. The Italianate villa became a beloved retreat for rulers of state, who flocked here to eat, drink and make merry. It was a Garden of Eden to all who beheld its exotic fauna, citrus trees and trick fountains – designed to sober up the clergy without dampening their spirits.

Vienna's foremost opera and ballet venue, the neo-Renaissance Staatsoper, is one of the finest concert halls in the world. Even if you can't get tickets to see a tenor hitting the high notes, you can discover its architectural brilliance and musical genius on a 40-minute guided tour. Tours (in English and German) generally depart on the hour between 10am and 4pm.

Picturesquely perched on a hill and set among beautiful gardens, this Renaissance pile was acquired in 1564 by Archduke Ferdinand II, then ruler of Tyrol, who transformed it from a fortress into a palace. Don't miss the centrepiece Spanische Saal (Spanish Hall), the dazzling Armour Collection and the gallery's Velázquez and Van Dyck originals.

Vienna’s Gothic masterpiece Stephansdom – or Steffl (Little Stephan), as it’s ironically nicknamed – is Vienna's pride and joy. A church has stood here since the 12th century, and reminders of this are the Romanesque Riesentor (Giant Gate) and Heidentürme (Towers of the Heathens). From outside, the first thing that will strike you is the glorious tiled roof, with its dazzling row of chevrons and Austrian eagle. Inside, the magnificent Gothic stone pulpit presides over the main nave, fashioned in 1515 by Anton Pilgrim.