In Sicily, visit Erice, a nice medieval hilltown close by Trapani. Be sure
to visit Selinunte (Greek temples) and the Rocche di Cusa not too far from
Selinunte(caves where they used to dig stones for the temple). Mozia is a
small island (few km square) along the cost between Trapani e Marsala
covered by archeological digs and a little museum with a great greek
sculpture founded there.
In Marsala there in the archaological museum where is preserved a punic ship (III cent. BC) and ... DON'T MISS the Marsala wine! :))
Don't miss the Villa Romana del Casale in Piazza Armerina: it is a roman villa with very well preserved mosaics (III-IV cent. AD). It is known as the place of the better preserved romans mosaics in the world! If you go to Ragusa, don't miss the archaeological museum of Marina di Ragusa. It is a little museum, just by the sea, and it is full of great treasures: many romans vessel sank there with many treasure inside!
Paolo don't miss Siracusa. Visit the Latomie (caves), L'orecchio di Dionisio (as suggested by an other ziners), The Duomo, the S. Giovanni Cataconbs and the important Archaeological Museum. A few km from Siracusa there are the great ruins of the Castel Eurialo (built by Dionisio, V cent.).
I won't tell you about the must that I assume you know (i.e. the temple valley of Agrigento, Taormina and so on).
Enjoy Sicily as I did 4 times!!!