Graz has the best-preserved old town in Austria outside Salzburg and Vienna, and it is much less crowded than either. The historic centre, a UNESCO site since 1999, sits on the river Mur beneath the Schlossberg, a rocky hill with a clock tower on top, and the roofs of the old town are a sea of red tile punctuated by domes and spires. Add a modern touch, the glass and steel Murinsel, an artificial island in the river, and the Kunsthaus, a blue bubble nicknamed the friendly alien, and the city has a mix of old and new that works.
Schloss Eggenberg, a short tram ride from the centre, is the other half of the listing. It was built in the early seventeenth century for Hans Ulrich von Eggenberg, a powerful adviser to the Habsburg emperor, and designed to represent the cosmos, with its state rooms, windows and towers laid out according to the calendar and the planets. Inside, the sequence of richly decorated state rooms is among the finest baroque interiors in Austria, and the Planetary Room, with its painted ceiling, is the one to see. The park outside has peacocks, which wander about like they own the place.
For riders, Graz is a gateway to Styria, the green heart of Austria, with its hills, vineyards and forests. Roads in every direction offer pleasant riding, including the winding routes of the Styrian wine country to the south, and the Schockl mountain and the Alpine foothills to the north. The city itself is busy, with trams and cyclists, and the old centre is largely closed to cars, so park at the edge.
All services are here: fuel, repair shops, hotels and restaurants. Try the local pumpkin seed oil, dark green and nutty, drizzled on a salad or even on vanilla ice cream, and a glass of Schilcher, a tart rose wine from the west of the region. The city is at its best in spring and early autumn.