Take a hike
Begin in Mariahilferplatz, the heart of Lend. This area has bloomed since Graz took its turn as European Capital of Culture in 2003, and is abuzz with bars and shops. Follow Mariahilferstrasse north, turn right on to Okonomiegasse, then cross the Mur via the city's most striking novelty. A metallic floating island connected to the banks by two bridges, the Murinsel was concocted by New York designer Vito Acconci as part of the 2003 celebrations. It was meant to be temporary, but has proved so popular that it lives on eight years later, its otherworldly shell holding a children's playground and café.
The Murinsel's easterly bridge leads you to Schlossbergplatz, where you find more cafés and chatter – before a right turn flips you on to the main drag. Sackstrasse flows south into the central square Hauptplatz, where Graz's most significant street Herrengasse takes over. Stroll slowly down this tram-tracked avenue, and take note, at number 16, of the Landhaus – a 16th-century Renaissance palace that is still the Styrian parliament.
East of Herrengasse, Kaiser-Josef-Platz has a farmers' market (daily except Sunday, 6am-1pm) where you can pick up a bottle of Styrian speciality kernöl (pumpkin seed oil) from €5.
Shops are closed on Sundays, so retail urges should be indulged early in the weekend. Semi-hidden at Kaiserfeldgasse 21, Laden 21 is one of the coolest of Graz's growing number of design stores. Part gallery, part furniture showroom, it sells quirky chairs and lamps. A kindred spirit back in Lend at Mariahilferstrasse 11 touts arty bags and multi-hued crockery.
Temptation also takes the form of Kastner & Oehler, a 1913 department store at Sackstrasse 7.
Lunch on the run
Kastner & Oehler also boasts Freiblick, a lovely top-floor café where you can gaze across the Unesco-lauded orange rooftops of Graz while eating beef tartare with toast (€12.50).
Most of the key cultural institutions in Graz are grouped together as effectively a single museum, the Universalmuseum Joanneum. A 24-hour pass is €11, a 48-hour pass costs €17 from any of the participating institutions. These include the Museum im Palais, at Sackstrasse 16, which showcases paraphernalia of the Styrian aristocracy, but the jewel is the Kunsthaus. An outlandish bubble of blue, it dominates the Lend district at Lendkai 1. Built by two British architects, Peter Cook and Colin Fournier, as part of the 2003 bonanza, this curved building is known as the "Friendly Alien" thanks to the 16 futuristic nozzles on its acrylic roof. At 10 minutes to the hour, when it "sings" to the city via a sound installation called Time Piece Graz.
Stay in Lend and sink a pint of Gösser – a Styria-brewed Austrian beer – at Die Scherbe, a bar with a bohemian vibe at Stockergasse 2 (00 43 316 760 654; scherbe.com).
Dining with the locals
Glockenspielplatz, Mehlplatz and Färberplatz are the hub of Graz's food and wine scene. Aiola City, at Mehlplatz 1, does an eccentric sepia tagliatelle (cuttlefish tagliatelle) for €18 – while Eckstein, at Mehlplatz 3, serves hecht gebraten (grilled pike) for €22. Gasthaus Stainzerbauer, nearby at Bürgergasse 4, offers local favourite gekochter tafelspitz (boiled beef with root vegetables) for €20.
Sunday morning: go to church
The Graz Dom, a 15th-century Gothic pile, glares at the city from its lofty address at Burggasse 3. The cathedral is open for services at 8.30am on Sundays (6.30am Monday to Saturday), its thick double doors giving onto an interior of surprising Baroque beauty. However, its most notable moment is found outside, on its south wall. Das Gottesplagenbild, a 1485 fresco, shows the city assailed by plague and assault from invading Ottoman Turks. Alongside, the mausoleum of Ferdinand II, Hapsburg emperor from 1619 to 1637, dazzles with gilded splendour.
Take a ride
Return to the river and pick up the Schlossbergbahn (daily 9am-2am; four departures per hour; €1.90) from its base station at Kaiser-Franz-Josef-Kai 38. This late 19th-century funicular railway carts you to the top of the Schlossberg at an improbable angle in just three minutes.
Out to brunch
No longer employed as defensive bastion, the summit of the Schlossberg has settled into happy retirement as a park. Several eateries take advantage of its wide-screen views, such as Aiola Upstairs at Schlossberg 2, where Sunday strollers snack on rocket salads (€10.20) at outdoor tables.
A walk in the park
The Graz Schloss was demolished in 1809 – an act of Napoleonic petulance after French forces had failed to capture it in an otherwise victorious war with Austria. But fragments of the fortress remain, including storage vaults now used as a theatre – and the Glockenturm, a 16th-century belltower. It peals 101 times, three times per day (7am, midday, 7pm). At the south-west corner of the park, you find the Uhrturm, a clocktower similarly rescued from Gallic ire. Its ornate yellow faces are the symbol of the city.
The icing on the cake
Take the stairs from the Uhrturm to Schlossbergplatz, then pick up a westbound No 1 tram (destination Eggenberg) from Hauptplatz. Three miles west of the river at Eggenberger Allee 90, Schloss Eggenberg is a 15th-century medieval palace clad in 17th-century Baroque garments). The trip is more than justified by the beautiful gardens.
Why go now?
Earlier this year, Austria's second largest city was anointed a "Unesco City Of Design" – an accolade only awarded to cities that boast established design and creative industries. Next month, the Steirischer Herbst festival (steirischerherbst.at) celebrates contemporary arts (film, dance, music, theatre, architecture) from 23 September to 16 October.
Ryanair operates the sole British air link, flying four times a week from Stansted to an airport that lies some five miles south of the city proper. Transfer options are plentiful. Taxis cost about €20 for a 15-minute drive, while bus services 630 and 631 take 20 minutes to deposit you at the transport hub of Jakominiplatz.
The railway station is a short walk from the airport and trains take 10 minutes, arriving at the main Hauptbahnhof, on Europaplatz. Tickets for this – and all single bus, train and tram journeys in central Graz – are also €1.90 (you can use the ticket repeatedly for one hour).
A three-day ticket – the Graz-3-Tages-Ticket – that covers all transport (and gives reduced entry to many museums) costs €9.90 from the tourist information office, Herrengasse 16.
Get your bearings
Graz is the capital of Styria, the second largest of Austria's nine states. Pitched 120 miles south of Vienna, it belongs to the part of Austria that faces away from the Alps, ebbing towards Slovenia, and the Adriatic beyond. The city is a tale of two river banks, the Mur separating the medieval kernel in the east from the once seedy but now aspirational Lend district in the west.
Sitting next to the station at Europaplatz 1, Hotel Daniel is a stylish budget retreat where doubles start at €59, room only. On the west bank of the river at Grieskai 4-8, Hotel Wiesler is a former five-star that has "downgraded" itself into a design hotel, complete with racks of vintage vinyl in the foyer. Doubles from €79, with breakfast. The Hotel Zum Dom does doubles from €124, room only. Slotted into the Palais Inzaghi, a renovated 14th-century mansion, it's at Burgergasse 14.Reuse content