Sicily

We spent 3 nights in Randazzo and enjoyed it very much. You could structure your trip to use both public transportation and a car. For example, we flew into Catania, took a bus to Siracusa/Ortygia (day trip to Noto), after a few days there picked up a car for Ragusa, Armerina, Agrigento, Segusta and Seliunte and then returned the car upon arrival to Trapani. From there used public transportation/driver for one day, to visit Palermo, Cefalu.

We had a car starting in Palermo (picked up the car at the airport after visiting Palermo and Cefalu) around the whole island - the opposite way that you are going. We left it in Catania to catch a plane to Rome. I do believe there are several tours out of Catania for the day up to Mount Etna. We drove up close but it was rainy and foggy that day. It has erupted recently so I would not pay in advance to a tour company unless they will refund your money.
We did Tamorina and did find it touristy but not large crowds(early May). It was a difficult drive up to the city and we did have to have directional help from a taxi driver. IMHO I would skip it. We did not do Catania but loved Ortigia/Siracusa. Ragusa and Trapani we liked as well.
I suggest you park outside of Palermo and take a taxi in. We were there for 4 days and loved it. We took the train from there to Cefalu for the day but since you are meeting the ferry again you could plan to stay there overnight and take the train to the ferry.
If I may make a suggestion I would book the Hotel Ambasciatori. It is a short walk to/from the train station. You then could return the car to the airport and take the train into Palermo. If you have Rick Steves Book there is a map to show you the hotel in relation to the Station.
I am not sure where you are meeting the Ferry but if it is in Messina you could make sure if there is a train from Cefalu to Messina.
I hope this helps in your planning.
Enjoy your trip

We are also senior, independent travelers. Our 10 day self-drive tour of Sicily looked like this:

1. Arrive Catania from Rome, drive to Taormina via Castelmola
2. Drive around the base of Mt. Etna with stops at wineries, back to Taormina
3. To Ortigia
4. To Ragusa via Noto
5. Ragusa - Modica - Scicli - Ragusa
   
6. To Agrigento via Villa del Casale
   
7. Agrigento to beach, then Valley of Temples in PM, stay Agrigento
8. To Cefalu’
9. To Palermo via Monreale
10. Palermo
11. Depart Palermo to Rome

We had a great trip, loved Sicily and would go back in a heartbeat! The only miss for us was Cefalu’ which we found very crowded, touristy, and unfriendly, plus parking was problematic. It was the only place in Sicily to which we would not return. We actually enjoyed our two nights in Taormina and the Greek amphitheater there is spectacular. Parking there was not an issue for us: We parked in a parking facility at the bottom of the hill and took the shuttle bus up to the pedestrianized old city. The Valley of the Temples at dusk was magical and a highlight of the trip. Palermo was enjoyable as well — just do not drive there! We dropped our rental car on arrival to the city and took a limo to the airport.

Have a wonderful trip!

I agree with a lot of the previous post. We are mid 70s, and have spent more than a year in Sicily during the last 15 years. I always drive here (we are in Sicily now, currently in Castellammare del Golfo, heading for Taormina area in a few days). The driving is certainly more aggressive and spaces are tighter, but there is a rhythm to it that works. I agree, though, that I wouldn't drive in Palermo. If you are a confident and safe driver you'll do fine. The roads are well sign posted and Google maps works great.
I suggest three ways to experience Mt. Etna. First, I would spend two nights in Taormina, and spend some time in the Greek Theater gazing out at Etna, just as ancient Greeks did two thousand years ago. If your hotel doesn't have parking, then park at either of the two parking garages. I prefer the parking deck at Parcheggio Porta Catania. From there it's just a couple minutes walk to Corso Umberto, the main pedestrian street of Taormina. Most people on this forum say Taormina is touristy, and it is, for good reason. We always enjoy it.
OK, second way to experience Mt. Etna... Drive to the lovely Etna village of Zafferana Etnea, which is known for honey. There are several routes to get there, I prefer the mountain roads starting in Linguaglossa, but there are easier ways. From Zafferana take SP92 through the lava fields to Rifugio Sapienza. The drive is other-worldly. When you get to Rifugio Sapienza, park the car and walk the rim of extinct Crater Silvestri. We've never been any higher up the volcano than this, never felt the need to.
The third way to experience what Mt. Etna has to offer is a wine tasting. For this you can't drive. Any hotel between Taormina and Catania should be able organize a winery visit for you. We have done it with groups of 6-10 people and it's always fun. We've been to Gambino, Benanti, and Murgo, but there are many others.
Hope this helps just a bit, have fun, safe travels!

We did our self-drive around Mt. Etna based on the route RS outlines in his guide to Sicily. We stopped for a tasting at Emilio Sciacca Etna Wine which I highly recommend. It is a small winery with a tasting room in a lovingly restored historic building, a direct view of Mt. Etna and Vincenzo, who was welcoming, kind and informative. We also had a tasting with full meal at Gambino. Gambino is a large, commercial winery with a huge tasting/dining area which was extremely crowded and loud. The experience was very impersonal, the best part being the view over Taormina. Two very different experiences! There are many other options but visiting wineries can definitely be done on your own if you so choose.

We have just returned from driving around Sicily. Flew into Catania, where we picked up the car, and drove to Syracuse. Stayed in Ortigia, where we parked the car in the Talete parking, using the Easypark app. From there we drove to Palermo. Our Airbnb, next to the modern art gallery, there was very helpful in reserving parking in a garage at €20 a day. You can use the Palermobilita app to buy a ZTL pass - €5 a day, which you can buy up to midnight on the day you use it - and you only need to buy one for the days you actually drive, so if the car is in the garage, as ours was for 3 days, only needed to purchase for the arrival and departure days. Visited Erice for an hour or so on the way to Tripani, it’s very close to the motorway. The castle in Erice was closed for renovations when we were there but thought Erice worth breaking the journey for the views. After Trapani (1 night) we drove to Agrigento via Mazara del Vallo, Selinunte and Sciacca - a long, but enjoyable day. Passed through Piazza Armerino on the drive back to Catania. Driving was generally fairly easy, and some stunning scenery.

Just realised I confused Erice with Enna