There are lots of restaurants and Cafes at and around the Hauptplatz where you can get high quality food.
The Gasthof-Restaurant Zum Brauhaus (http://www.brauhaus.co.at/) with outdoor seating in good weather. Serving traditional Austrian food and open for breakfast lunch and dinner.
Casa Mulino a Italian Restaurant with romantic interior and outdoor seating in summer. Open for dinner only but something you must not miss.
Abendrestaurant im Schloà +43 3332 61850 with traditional Austrian high quality food. Located inside the castle in the SchloÃpark, it is one of the best locations.
Restaurant- u Vinothek PuÃwald, Grazer Str 18 +43 3332 62584, one of "the" best restaurants in terms of quality of food you can find in Hartberg.
The Cafe Sonne, with breakfast and a small lunch menu.
There are many more restaurants. Just explore the streets and alleys of Hartberg, you won't be disappointed.