Southern Italy and Sicily

There's more than enough to see in Sicily to fill 2 weeks. I suggest focusing your time there. You could fly into Palermo and out of Catania (or vice versa) and work your way across the island, or you could fly in and out of Palermo or Catania and make a complete circle around the island. The better of those 2 options would depend on which places you decide to visit. For example, if you want to follow a route similar to the RS Sicily tour, then flying into one and out of the other would work well. If you want to visit both Agrigento and Cefalu, then making a circle might be better. Lots of good options.

Should you decide you want to split your time between Sicily and the mainland, I suggest you limit your Sicily time to a couple of destinations on either the east or west coast, such as Taormina and Siracusa (east) or Palermo and Trapani (west).

I totally agree with Frank. I have very little interest in Greek ruins (of which Sicily has several), and 18 days (admittedly without a car) was too little time for me in Sicily. Two weeks is a fairly short visit there, and you can also easily fill two weeks in the southern part of the mainland (Naples/Amalfi Coast/Puglia, etc.) It would definitely not be my choice to try to combine them on a trip of that length. You'd either be flying to and from Sicily (dealing with airports twice) or there would be a lot of time on trains or behind the wheel of a car.

Thank you for your replies. I will look into Agrigento and Cefalu. As I am not familiar at all on things to see and do in Sicily.
Cheers,
Ingrid