Sicily parking

Ask whoever you’re renting the Airbnb from about parking. Most streets are pedestrian only, but there is a road along the outside of the island. If need be, once you cross onto the Ortigia , turn left, there are a couple public lots. I looked up public parking lot locations before going there and plugged the addresses into my GPS. It took me directly to it. The pay parking machine only took €1 and I believe €2 coins; Nothing smaller. Since I was there only a few hours, I didn’t pay attention to the pay vs free times. Assume about €1 per hour to park in the public lot. Different lots can have slightly different prices. For the rest of the towns we stayed in, we chose hotels or B&Bs with parking.

If the listing did not address parking, asking the owner/host/manager is the way to get a good answer to the question.

As you cross the short bridge into Ortigia island you will turn left toward the Talete Parking Garage to the northern side of Ortigia. The image is below.
https://goo.gl/images/B781Qd
The parking fee for the Talete parking (and also other parking lots in the city) is below. Basically 1€ per hour or 10€ for 24h.
http://www.siracusando.it/aree-di-parcheggio---tariffe.html
Your itinerary is good, I think. Ortigia for 4 nights might be more than you’ll need, but you can use that base for a day trip to Noto for a day and of course to see the archeological park of Siracusa, in the mainland part of the city.

Yes, follow Roberto’s directions to a large parking area on the north end of the island. There is also parking in Siracusa just before you drive over the bridge to Ortigia. There are a few small parking areas around Ortigia but you would be very lucky to find a space free. We spent a week on Ortigia and wished we could have stayed longer. We were not issued any parking
permit. Don’t miss the daily( except Sunday) outdoor food market at the same end of the island as the parking lot.
As far as your itinerary, I hope you are planning on visiting The Valley of the Temples in Agrigento, an amazing antiquities site, while you are in the Western area of Sicily.
And during your time on Ortigia, visit the Greek Theater in Siracusa. Very impressive.
Locanda di Collegio is excellent for dinner in Ortigia.

Here is more helpful information about parking at Talete on Ortygia.

http://www.comune.siracusa.it/images/doc/Mobilit%C3%A0_e_trasporti/Parcheggio_Talete.pdf

Parking in Cefalú has normally been a problem for me. There is a multi story near the train station (was quite expensive). Enterprising people near the beach let people park on their large grounds (it was about €6 a day, but I don't think they did overnight parking) and the other option was parking near the marina, but this is a fair walk from the city centre.

I went 4 years ago for 2 weeks, April/May. I flew into Palermo a couple days - there are beautiful places to visit and a great market. I took the bus to Monreal for 1/2 day. Then I spent 2 nights in Cefalu by train, returned to Palermo and picked up a car. I also stayed in Castellammare del Golfo, day-tripped to coastal towns, Segesta and Selinunte. The coastal towns were very quiet on Sunday and most sights were closed. Check what is open on Good Friday and on Easter Sunday and Easter Monday as well. Then I spent a day at Agrigento, overnighted in Piazza Amarina, went to Villa Casale de Romano and ended the day in Ortygia for 6 nights. I dropped the car at Catania airport and flew to the mainland. The first night (maybe two) I parked in the big lot on the Ortygia side of the bridge and it was free. After that I got a parking permit from my hotel and was able to park in the area. I never encountered heavy traffic in/out of Ortigia. I went into Catania once for the WWII museum (worth it) and traffic was very congested.

BTW driving was easy, the roads were in good condition and there were tons of wildflowers. My only problem was that I didn't have GPS and wasted some time.