Sicily - how to get there from eastern US?

what did google flights say? If NC is North Carolina, you would need to get to Europe and change. But there would be many possibilities.

Plug your airport and PMO for Palermo or CTA for Catania into Google Flights to see options for your specific dates.
Will this be a trip to the mainland as well?

We flew from west coast to east coast to Rome and transferred to a flight to Palermo. Easy enough.

Go to skyscanner.net, I put your departure and destination airports and wait. It’s the ONLY website I use to search for airline tickets.

I recommend flying. Use Google flights and/or skyscanner to plan your flights and find the best deal and set of flights for you and your schedule.

Do not take one of the rowboats being offered out of Palm Beach, FL. It’s a bit choppy and takes longer than advertised and they don’t even offer a bag of peanuts during the journey.