Innsbruck

The Goldenes Dachl — a balcony oriel sheathed in 2,657 fire-gilded copper tiles, commissioned by Emperor Maximilian I around 1500 — is the visual symbol of the city. It anchors the medieval Altstadt, a small grid of late-Gothic and Renaissance burgher houses where the arcaded ground floors still front the Herzog-Friedrich-Straße. The Stadtturm city tower opposite gives a free panorama over the red roofs to the Karwendel wall above, and the Helbling-House at the corner is one of the most photographed rococo façades in the Alps.

The Hofburg Innsbruck, the Habsburgs' Tyrolean residence, was remodelled by Maria Theresa in the 1750s and the state apartments are one of the country's three great imperial interiors alongside Vienna and Schönbrunn. Directly opposite, the Hofkirche houses Maximilian I's cenotaph — an empty marble tomb surrounded by 28 over-life-size bronze figures of the emperor's ancestors and contemporaries (the Schwarze Mander), the most ambitious sculptural ensemble of the German Renaissance.

The Nordkettenbahn cable-car system — designed by Zaha Hadid Architects with four sculptural stations along the route — climbs from the Congress in the city centre to the Seegrube at 1,905 metres and the Hafelekar at 2,256 metres in twenty minutes. It is one of the very few cable cars in the world that begins inside the city's pedestrian core. The Hafelekar terrace looks straight down on the old town and out across the Tuxer Alps; the Alpenzoo (the highest-altitude zoo in Europe) sits on the line between the two stages.

The Bergisel hill at the southern edge of the city is both an Olympic venue and a battlefield memorial. The Bergisel ski jump — rebuilt by Zaha Hadid in 2002 — is a working World Cup venue and a panoramic restaurant; the Tirol Panorama museum at its foot houses the giant 1809 Bergisel panorama painting that commemorates Andreas Hofer's Tyrolean rising. The Olympic flame from 1964 and 1976 still rests at the jump's base.

Schloss Ambras above the eastern edge of the city was Archduke Ferdinand II's Renaissance residence and houses what is now the oldest surviving princely art collection in Europe. The Spanish Hall, the Heldenrüstkammer armoury of personalised armours of Renaissance princes, the Kunst- und Wunderkammer cabinet of curiosities and the Habsburg portrait gallery occupy a complex of upper and lower castles in a formal park.

Innsbruck is one of very few cities in which a serious ski resort opens directly from the urban transit network. The Stubaier Gletscher, Axamer Lizum (the 1964 and 1976 men's downhill venue), Nordkette, Patscherkofel, Schlick 2000 and Kühtai together form the Olympia SkiWorld Innsbruck, and a single Innsbruck Card or Ski-plus-City Pass moves a visitor between them on free shuttle buses. The Karwendel above the city is the heart of Austria's largest nature park and a major summer hiking destination.

Tyrolean cooking is mountain food at its most assured. Tiroler Gröstl (a pan-fried potato-and-bacon-and-onion dish topped with a fried egg), Speckknödel and Käsespätzle, the air-dried Tiroler Speck and the dessert Kaiserschmarrn are everywhere; the Markthalle on the Innrain holds the daily produce market; and the Stiftskeller in the old Wilten Abbey serves a strong baroque-cellar version of the tradition.