Tyrol’s capital is a sight to behold. The jagged rock spires of the Nordkette range are so close that within minutes it’s possible to travel from the city's heart to more than 2000m above sea level and alpine pastures where cowbells chime. Summer and winter activities abound, and it’s understandable why some visitors only take a peek at Innsbruck proper before heading for the hills. But to do so is a shame, for Innsbruck is in many ways Austria in microcosm: its late-medieval Altstadt is picture-book stuff, presided over by a grand Habsburg palace and baroque cathedral, while its Olympic ski jump with big mountain views makes a spectacular leap between the urban and the outdoors.