Various airlines and airline groups have flights to Italy with connections to Palermo and Catania.

Eurofly runs direct flights between New York JFK and Palermo 2 times a week. You can get tickets for these flights also through Meridiana

Companies offering flights to Italy:
Air Canada
Alitalia
Continental
US Airways
American Delta Airlines
Canadian Airlines
United Airlines
TWA

Please check the airlines websites for information regarding schedules, price and availability, or to book on-line.