In Agrigento you should visit the Archeological Park of the "Valley of the temples". On-line there is also a virtual reality tour of this historical site.

When in Sicily you should eat Cannoli and drink Malvasia of Lipari. At your home you can treat yourself with a Caponata, a versatile dish of which exist also a quick (and poorer) version.

Read some short history of the sicilian Mafia and for something more entertaining try Peter Robb's book "Midnight in Sicily" and its reading notes.