The city of Graz has a useful page (in German) on walks in and around Graz which can be reached by public transport.
“10.000 Schritte in und um Graz” is a new book (published as part of Graz’s Lets Go campaign) and contains 15 walks around Graz all reachable by public transport. Ranging from 6 to 8 km and with full colour descriptions. Available from bookshops for €20 or the public library. You can also see the following 5 hikes and their full descriptions here.
1: Over the Rosenhain to AndritzTour
2: Via Reininghaus on the BuchkogelTour
3: From Andritz to the StephanienwarteTour
4: From St. Veiter Schlössl to the Alpengarten RannachTour
5: From Schloss. Martin to Straßgang
There is also a good booklet ‘ Wander-, Walking- und Fahrradguide‘ which can be picked up for free at the tourist office or downloaded here with lots of good walks and hike suggestions.
I can also recommend this book (available at Moser bookstores or the public library) ‘Spaziergänge in Graz und Umgebung mit Bus, Bahn und Bim‘.
For longer hikes, Styria public transport ‘Verbund Line‘ has a set of brochures with good maps and transport connections which can be picked up at the transport office – Mobil Zentral, Jakoministraße 1 or downloaded here and more reachable by train here.
‘Dieters Geheimtipps‘ has several longer hiking trips in Styria all reachable by public transport. He includes a good description (in German) and links to nearby cafes and other useful tips. And click on the description photo in each hike to see more photos and a map.
The Alpenverein’s office on Sackstraße 16 (opposite Kastner and Öhler) are experts on hiking trails. They have lots of hiking maps and can offer advice on which are accessible by public transport.
On weekends and public holidays you can take advantage of the Freizeit-Ticket to travel anywhere in Steiermark for €11 for the whole day.