Renting car and driving in Sicily

Just google "ZTL" to read up about avoiding tickets and you'll be fine.
You will need an international driving permit, obtained at AAA for about 20 bucks.

Yup
Get an intl permit at AAA, carry it and your US license.

Driving in the big cities is pretty tough (Palermo especially) but it sounds like you won’t be doing that. Driving anywhere there is traffic is different than in the US - more chaotic. It’s doable, just pay attention and don’t expect other drivers to follow the same rules they do at home. A 2 lane roundabout can easily have 3 cars and 2 motorbikes across. It works fine. But do get good insurance on the car - a minor scrape or bumper hit is quite possible.

Roads in the countryside are good and uncrowded.

Some old villages and town centers have very narrow streets. Like one car barely fits narrow. Often parking a few blocks out and walking in is easier than trying to navigate it.

If you need an automatic transmission be sure to specifically reserve one. Unlike in the past they seem to be easily available- but the default is stick shift so for auto reserve ahead and double check.

Great tips above: learn to recognize ZTL (limited traffic zones) signs so that you can avoid them and the fines they may impose; get an international driver's license.

Maps: use a good mapping app, such as Google Maps - which worked perfectly for us in Sicily. Download the maps for "offline use" so that you don't need wifi or a data plan.

Other tips:
Pre-plan your parking to the extent you can for hotels or major sites.
Bring some small change for highway tolls or parking meters.
Allow extra time over what you think a distance might require, especially in towns.

Most of all, temper your driving with an attitude of "ci arriveremo quando arriveremo" - we'll get there when we get there.

The road (E90) from Messina to the exit for Capri Leone (just as you’re exiting a tunnel) is a good road, and a toll road, so have some change. The SP157 from the E90 to Capri Leone is two lanes and appears to have a number of sharp turns going through the hills. Other than having to drive a little slower, you should have no trouble. The ZTLs should be pretty easy to spot. Don’t speed; better to be safe than incur a traffic fine. If you try to be nice to let somebody in, a few others may take advantage of your kindness. A GPS or google maps downloaded for offline use come in handy. I didn’t find the roads to be that well marked, once off the main road.

As already mentioned, pre plan your parking. If you know which towns you’ll be visiting, look up the public parking lots ahead of time. I plugged their addresses into my GPS and went right to them. The machines at the lots I used only took €1 and €2 coins; nothing smaller.

We found driving in Sicily less crazy than driving in other parts of Italy, especially Calabria. The roads were in good condition and easy to navigate.

We used a Garmin GPS for traveling around and it was quite effective. We were staying in Taormina and during the coming and going from there the GPS screen looked like a dish of linguine because of the narrow switchback roads.

We used Autoeurope from their location at the Catania Airport and the entire process was easy, easy.

Buon viaggio,

See also https://www.ricksteves.com/travel-tips/transportation/driving-europe-tips and related articles linked from the sidebar.