You can see the wine hills around Seggau castle from far off, and that tells you everything: Leibnitz is the heart of the South Styrian wine country. The town has good outdoor cafes serving local and international dishes alongside the region's excellent wines, and hosts wine celebrations, music and cultural events throughout the year.
It is a good base for exploring the area. The ruins of Flavia Solva, a Roman city, are a short walk away. The Weinlehrpfad — a wine education trail run by the local winemakers' school — winds through the vineyards. The Sulmflussbad offers swimming in summer, and there are plenty of hiking routes in the surrounding hills.
The real draw for most visitors is the South Styrian Wine Road, which winds through the terraced hills south toward Slovenia through some of Austria's finest Sauvignon Blanc country. Schloss Seggau above the town is worth the climb for the views and the estate wines.