I agree with Flavio about Umbria, it is a very nice region. You'll find history (many medieval town, art (very beautiful church), important religions site (related to S. Francesco and S. Rita), nature and, not at last, a good cooking !! Another region very interesting for history, art and cooking is Sicily. It is not expensive but it is not close to Lazio. In Sicily you'll find Greek archaeological site (The Temples Valley of Agrigento, The Temples of Selinunte and Segesta), Roman Mosaic of Piazza Armerina, nice town (Taormina, Monreale and Erice), nice city (Siracusa, Palermo, ...) and, obviously, good food ! In October in Sicily you'll find a good weather .

Have a good trip.

Marco from Milan, Italy.