The Borgo di Montemigiano has excellent hiking with breathtaking views. Simply exit the back gate (formerly the front gate), pass Angelo and Marissa's garden (say "hi" to Cavalo, Angelo's beloved horse) and follow the well maintained trail to the left. Handy signs have been installed recently, indicating distances and directions.
One of our favorites is to hike the ridge west to the ruins of a medieval convent, Sant'Anna, about 3km away from the Borgo. The convent shares the hilltop with large towers so its easy to see which hill (and signs point the way).