We are visiting Sicily mid-Oct. for a week, flying into Cantania & flying out of Palermo, and renting a car.. Suggestions about where to stay & what to see? Bill
Go directly to Taormina or Siracusa (opposite directions). Tight for a week, but: Siracusa or Taormina, Villa Romana del Casale, Agrigento, Trapani/Erice, Palermo, Segesta, Cefalu.
Here is a website that I used in researching Sicily and it has hundreds of links to detailed info about all of Sicily.
Best of Sicily
Here's my VERY detailed trip report from spring 2014, which should give you some ideas: https://community.ricksteves.com/travel-forum/trip-reports/sicily-palermo-caltanisetta-siracusa-taormina