Don’t miss...

Countryside

Schladming A hiking oasis in the Dachstein Mountains, home to Styria’s highest peak and over 900km of bike routes. Ride a gondola up to the Dachstein Glacier to get close to the ice. www.schladming-dachstein.at

Admont Abbey This Benedictine Abbey has an eye-catching Baroque design and the largest abbey library in the world. It sits on the border of Gesäuse, Austria’s newest national park. www.stiftadmont.at

Mariazell Basilica Compelling ecclesiastic hub that’s long been drawing pilgrims; handy for hiking too, given its mountainous location. www.basilika-mariazell.at

Stainz Castle Arguably Styria’s finest schloss, Stainz presides over a landscape of vineyards and orchards. There’s a fascinating museum dedicated to hunting and agriculture inside. www.museum-joanneum.at

Klimazukunft-wegs This new 9km hiking circuit winds gently through lush Pöllauer Valley Nature Park, with info stations addressing climate change issues en route. www.naturpark-poellauertal.at

Kunsthaus Lovingly known as the ‘friendly alien’, this contemporary art museum is housed in a remarkable biomorphic glass-skinned structure that seems to float amid the old town. www.museum-joanneum.at/kunsthaus-graz

Eggenberg Palace Built on a medieval original, the construction of this Renaissance gem is based on the Gregorian calendar: four corner towers, 31 rooms on each floor, 24 state rooms with 52 doors, 365 windows. Catch the tram here and enjoy the surrounding parkland afterwards. www.museum-joanneum.at

Murinsel Part island, part ship, this unique creation of glass and steel was conjured up by American artist Vito Acconci. The structure reclines in the River Mur, connected by footbridges to both banks. It has an amphitheatre, café and shop, hosts events and lights up at night. Unmissable. www.murinselgraz.at

City

Schlossberg Catch the funicular up to Graz’s hill-top castle. Look out for the 16th-century Clock Tower, the city’s icon, and don’t miss the Grazmuseum Schlossberg or the views from the SKYBAR. www.schlossberggraz.at