Southern Italy Trip in 2020

The best site for flight research is www.skyscanner.com.

Aegean flies non stop from Catania to Athens; not sure if every day.

For Brindisi, search flights from Brindisi to "everywhere." Then pick Italy [or go direct to IT]. That will generate a list of cities with flights, non stops first.

You may be having trouble because the largest airport in Sicily is Catania, not Catonia (not all websites have Google's helpful "did you mean?" feature).

To find out who flies where from a particular airport, a great start is the airport's Wikipedia page. Here's Catania: https://en.wikipedia.org/wiki/Catania%E2%80%93Fontanarossa_Airport#Airlines_and_destinations. However, flights can be as infrequent as once a week, and a "seasonal" flight can be for 7 months of the year or just 2-3. So, use Skyscanner to find flights actually operating on your travel dates.

Getting from Naples to Brindisi can be done by train or bus. FlixBus has two buses daily. Either way, it’s a 5+ hour trip. Flying from Brindisi to Catania is also a long trip. Most economical way is Alitalia but there are no direct flights. They all require a change in Rome. Similarly, there are no direct flights to Athens from Catania. Alitalia has a number of flights but they all go through Rome.

Consider changing your path, see if this would work for you.

Fly to Rome, with a connecting flight to Brindisi. Make sure this is all on one ticket.

Brindisi>Athens.

Athens>Catania.

Catania>Naples

Fly home from Naples.

Thank you all for your help. The skyscanner website is most helpful.