Many of the larger cities like Parma, Bologna, Forlì, for example, have bus service into the countryside. Bologna is a major train station with Eurostar, as is Rimini.If you can, rent a car and take any of the many roads that branch off the Autostrada and head south into the Alpennine Mountains where you will find hot spring spas, ancient castles protecting mountain passes don't miss Castello Torrechiara, near Parma.

Side note: While taking the train south from Milan, don't forget to catch a glimpse of the Domo perched above Bologna in the south. It is especially interesting at sunset.