The old city of Graz is small enough to cover entirely on foot. Most of the sights are within a 15-minute walk of Hauptplatz. The Schlossberg is a short walk from the centre; the funicular and lift make the climb effortless if the 260 steps seem unappealing.
For longer distances, the city has an efficient tram network. Tram 1 runs west from the centre to Schloss Eggenberg. Trams 3, 4, 5, and 6 serve the rest of the city and the main train station. Single tickets are available from machines at stops; the 24-hour pass is good value if you are making several journeys.
Cycling is popular and the city has a reasonable bike-share network. Car hire is available at the airport and at the main train station, but is only useful for day trips into the Styrian countryside — the old centre is largely pedestrian.