3 Days In Sicily

Since you'll be all in that area, it would be a shame for you to miss the Almafi Coast. The towns of Amalfi and Positano are amazing. Also the mountaintop town of Ravello is beautiful with beautiful views. Sorrento, (Between the Amalfi coast and Naples) has the best lemons in the world and therefore the BEST Limoncello. If you try the Limoncello, be sure to also try the Creme' Limoncello. A little milder and yummy. If you like it, be sure to buy some, the Creme' Limoncello is hard to find in the states. Have fun!!!

You can easily drive in Sicily, best in a smaller car. My friends usually rent a Fiat Punto.

Why not stay a couple of nights in Licata or Canicatti? You can check a booking service like booking.com for availability, price, amenities, free parking, and reviews by previous guests.

Are you spending 4 nights in Sicily? Where and how are you arriving and leaving? Are you planning on also spending time in Palermo or visiting other sights in addition to your family towns? If you don't want to stay in Palermo you could stay in Cefalu, a small town with a beautiful cathedral, on the coast nearby and a bit closer to your towns. Alternatively, you could stay in Agrigento, even closer to your family towns with the added benefit that the Valley of the Temples is located there, giving you the opportunity to see the ancient site. According to google maps it's about a 2 hour drive from Palermo to Canicatti and 2.5 to Licata. Do you want to drive this each of the 3 days? Agrigento, about 2 hrs from Palermo, would cut about an hour from your drive to your towns, but you have to get to Agrigento first. You need to think about whether you spend your entire time in the family towns or if you plan to see other sights as well and how much time you want to spend in the car, and then you can decide where to stay.

As far as driving in Sicily, it should not be a problem. We spent a month there in 2013 (we were in our late 60s at the time) and had no problem driving around the island. We rented a car at the Palermo airport and returned it there before taking the train into Palermo to spend a few days there. Would not try to drive in the city of Palermo but had no problem with the highway around it.

You can dismiss Cindi's advice about the Amalfi coast. It's not in or near Sicily.
Licata and Canicattí are far from Palermo (almost 3 hr drive), you can travel there on a day trip from Palermo, but you won't have much time. In that area you could visit Agrigento and the Valley of the Temples. Maybe you could spend the night there to have more time, but I realize you are in Sicily for only 3 nights.
To visit Western Sicily I like to base myself in the village of Scopello and drive to places from there.

I think Cindi was referring to the OP's mention of going to Naples during the trip. But Roberto is right, not near Sicily.

My VERY detailed report of my Sicily trip is here, including my experience with driving. It's not "hard," but it is different from driving in the US: https://community.ricksteves.com/travel-forum/trip-reports/sicily-palermo-caltanisetta-siracusa-taormina

Since Roberto says the towns you are interested in are several hours from Palermo, I would NOT recommend staying in Palermo. In addition to the commute time, driving in and out of Palermo isn't easy. So, pick up a car at the Palermo airport and base yourself closer to the towns you want to see. Of course, depending on when your flight back is, you may need to stay in or near Palermo the night before your flight.

If you don't mind being an hour or so from your towns, the agriturismo I used near Caltanisetta was a lovely place to stay.

To find flights from Rome to Palermo and from Palermo to Naples, start with Skyscanner: http://www.skyscanner.com/. If you want to book on Alitalia, I found better prices by using their International site instead of their US one. Remember that Alitalia allows one checked bag as part of the base fare, so it's not necessarily more expensive than a "budget" carrier.

To emphasize Harold's advice, do not drive in Palermo unless you have to. It's not particularly difficult but traffic moves incredibly slowly much of the time and you won't know which streets to take to avoid it (if indeed that is possible).

Assuming you are flying in and out of Palermo, rent a car at the airport and return it there. Look for agristurisms near those towns. I found driving through Agrigento to be a pain. Driving between towns was easy, roads were good. Be sure to have a good map with you. Are you okay with manual transmission? If so, you can get a small car. The automatics are usually the larger cars, and will be more expensive.

I was in Sicily in late April last year - the wild flowers were incredible.

Thanks to all that have replied so far!

I'm thinking that perhaps we might now rent a car at the Palermo airport to drive and and explore. We would stop in Canicatti and then spend a night in Licata. Where to go next would be the question. Do we head west for another night or east towards Catania and fly to Naples from there?

Flights from Catania can be delayed or cancelled if Mount Etna is smoking. Since you only have three days, I would stay on the western side of Sicily. It may take more than a day to find family connections, so two nights in Licata might be best, go back to Palermo for the last night before your flight.