If you speak a little Italian (or can pick up a little bit by the time you go), you *must* go to Sicily. Especially the western tip and the southeast! It's an amazing place -- nice people, cheap food/hotels, out of touch with the more modern world. Take the train all around the island, go to the smaller islands -- all without the maddening crowds of the north (anything north of Naples). After Sicily, the Amalfi coast is expensive and less impressive.

(of course, if you haven't seen the cities of the north yet, stop by those too sometime)