Sicily in March/April

We used auto Europe in Sicily, and it was very easy
https://www.autoeurope.com/contact/

Regarding flying. We flew into Rome and then instead of rushing to fly to Catania, stayed at the Rome airport Hilton and got so much needed sleep so we could start our vacation rested, then took an early flight to Catania.
NOTE: the earlier you book the Rome airport Hilton, the less expensive it is.

We didn’t go to Palermo, but the rest of the sites you mentioned are great.

If you have time, I would add Villa Romana, it’s in Rick Steves book, i.e., the bikini girls athletes mosaics. Pretty amazing.

We rented through Avis at Catania airport for our trip.

Just here to say that I was in Sicily in May a few years ago and it was shockingly chilly. I had packed dresses/ light clothing and needed to buy a sweatshirt while I was there. That ocean breeze REALLY made things cool so I recommend packing at least a few warmer layers.

I have been in Sicily twice, at the beginning of November and also in March. As a resident of Minnesota, I imagined that Sicily would provide a warm, Mediterranean respite from cold weather. NOT! Regardless of online weather predictions, I found that while some days were mild and only required a light sweater, evenings were always chilly and some days were downright cold - especially on windy days along the coast and up on Mt. Etna. I needed and used all my layers - long-sleeves, fleece jacket, and even a light-weight quilted jacket! My warm cashmere scarf was appreciated, along with gloves. Maybe you will be luckier than I was in terms of weather, but bring layers in case.

You can explore actual, historical, day-by-day weather data for lots of places on the website timeanddate.com. I like to look at the most recent five years since weather does vary a lot.

Palermo weather -- March 2023

Use the pull-down box at the right, just above the graph, to change the month and year displayed.

Use the Search box at the upper right to change the location.

If the weather's at all chilly, locations near the water may call for layers because of the breeze.

I’m glad to see in the comments that I’m not the only one who was surprised by Sicily’s chilly May weather! Even if you get a warm day for the beach the water will be very cold. Fair warning.

With 3-4 weeks you ought to be able to experience Sicily pretty thoroughly. The hill towns in the southeast (including Noto) would make for a nice few days. I would also give yourself about 4 nights each in Ortigia and Palermo. Both were absolutely brilliant. With the cool weather being a factor, I would not devote much time to places like Taormina or Cefalu. Not mentioned was Villa Romana del Casale, which I would basically consider a cardinal sin to miss. It’s also a logical stopping point between the southeast and the western half of Sicily. If you’re into ruins, I also enjoyed Morgantina nearby.

Thank you for all these great ideas and feedback! Much appreciated.