The hills and the mountains in the south of Reggio Emilia are definitely worth a visit, but you can reach some areas only if you have a car or a motorbike. The main locations will be served also by public transports bus. If you travel by bus make sure to buy your return ticket before leaving Reggio and to check the time tables, as there's no public transport in the evening and in the night.
Some places you should visit if you're in Reggio Emilia:
Pietra di Bismantova
Canossa and Rossena castles
Torrechiara in the province of Parma, next to the border with Reggio Emilia