Shadows Slant Over Innsbruck’s cobbles as the city shakes off its slumber and wakes for another day. In its cafes, locals gather for their morning constitutional – a cup of black coffee and a slice of apple strudel, baked at dawn and served piping-hot. As they tuck into breakfast, sunlight creeps along pavements and onto facades painted in pastel pinks, mustard yellows and duck-egg blues. North of the Altstadt (Old Town), cable cars buzz up the hillsides, ferrying walkers to an early start among the spiked summits of the Nordkette range.

More than 200 miles west of the Austrian capital Vienna, Innsbruck is a city where life is framed by the mountains. Hedged north and south by peaks, it guards one of the most ancient trading routes over the Alps, the Brenner Pass. For centuries, pilgrims, pedlars, traders and troopers have travelled through here on their way across the mountains, using Innsbruck’s namesake bridge to cross the Inn River en route to Italy and the Mediterranean beyond.

Innsbruck grew rich by controlling the flow of trans-mountain traffic. As capital of Tyrol, it served until 1665 as an alternative seat of power to Vienna for the Habsburg dynasty. Even now, long after its imperial star has waned, the town still cheekily bills itself as the ‘Capital of the Alps’. Habsburg influence dominates the elegant Altstadt. Boulevards lined by mansions and merchants’ townhouses radiate from the city’s heart, and many buildings are richly decorated: swashes, scrolls and curlicues embellish their Baroque facades, like flourishes on a wedding cake. Often, the architecture contains echoes of old glories: the imperial double-headed eagle is a common motif, adorning everything from shop signs to door knockers.

Inevitably, it’s the city’s royal buildings that impress most. The hallways of the Hofburg Palace are lined with Old Master paintings and objets d’art, and its ceilings emblazoned with frescoes that play games with the eye – conjuring curves where none exist, or seeming to open into the heavens. Nearby, on Herzog-Friedrich-Strasse, stands the Goldenes Dachl (Golden Roof), built for Emperor Maximilian I in 1500 as a royal box from which to watch festivities in the square below. Crowned with 2,657 copper tiles that flash and shimmer like fish scales in the sunlight, it’s a striking reminder of Innsbruck’s glorious past.

One man who has an unusual insight into the city’s history is Peter Grassmayr, whose family owns Austria’s oldest bell foundry, founded in 1599, just south of the city centre. Grassmayr bells have been chiming out from the city’s church towers for four centuries, and are now shipped to temples, chapels and sanctuaries across the globe. ‘We make bells for eight different religions and 50 countries.’ Peter explains, as he strolls around the foundry’s bell garden, where a collection of the company’s historic bells now reside in hushed retirement.

‘We might be in the middle of the mountains, but our bells can be heard as far away as Jerusalem, Australia and Japan!’ For all its architectural pomp, these days Innsbruck is a place that’s more popular for the outdoor pursuits that take place beyond its urban core. It has hosted the Winter Olympics twice – in 1964 and 1976 – and few cities have such a main line to the mountains. A futuristic funicular, designed by star architect Zaha Hadid, joins up with two cable cars to whisk hikers, skiers and snowboarders from the Altstadt’s squares into the heart of the Nordkette range at more than 2,000m, taking 20 minutes in all. At the top, a viewing platform overlooks the city’s rooftops — a sea of spires, domes and terracotta tiles, backed by black peaks.

But there is a price for such a view: as the cable car glides to a halt and its doors whoosh open, a blast of wind whips up from the valley below, sending hats and gloves flying as it howls across the summits. Most people are prepared, tightening hoods and zipping up fleeces as they begin the trek back down towards the city. In an hour or two, they will be rewarding themselves with mugs of hot chocolate and slices of torte in one of the Altstadt’s old-world cafes.