There are lots of things that are worth a visit.
A good starting point is the Hauptplatz, the main square and centre of the town with the local church open every day, the Karner build in the 12th century and used to be storage place for human bones and the nicely refurbished Rathaus town hall. It's the meeting point for locals in summer with lots of restaurants and bars with outside seating areas.
Even though Hartberg is not very big you can find two parks. The Stadtpark and the Bergpark with a castle that was refurbished not that long ago. In recent years it became more and more attractive as a weddings venue for locals.
If you are a fan of nature you won't be disappointed by the Gmoos, the last big moor in east Styria and since 1992 a protected natural reserve habitat of lots of wildilfe. There is a walking trail around it with many peacful places to sit down and ejoy the nature.
Not far from the town centre 3km near Löffelbach you can find Villa Rustica, the ruins of a villa build by the Romans around the 2nd century a.c.