Austria’s international reputation has been eternally romanticised by The Sound of Music, but it isn’t all cowbells, sleigh bells and schnitzel with noodles. Most visitors come for one of two reasons: to visit the Alps, or to lose themselves in the urban oases of music, high culture and elaborate architecture scattered around those snow-blanketed peaks. The glitz and glamour of Vienna, with its world-famous opera house and grandiose palaces, contrasts with the rustic appeal of ski villages such as Alpbach and Lech. Somewhere in between those two extremes are the cities of Innsbruck and Salzburg – Alpine gems, where you can browse galleries packed with Old Masters in the morning and be slaloming down a well-groomed piste by lunchtime. Few countries offer such a heady combination of culture and adventure.