I agree with Chris, you can visit Noto, Modica and Ragusa from Syracusa.
I'd suggest staying in Ortigia, the historic center of Syracuse.
I truly enjoyed my 5 night stay at Albergo Domus Mariae. My room had a small balcony with an amazing view of the sea.
The room rate includes a fantastic hearty breakfast buffet which is served across the street at the Domus Mariae Benessere (more expensive hotel). Ortigia became one of my favorite places, I could have stayed there forever if I didn't have family back home!
Make sure you eat at 'Sicilia in Tavola', my favorite restaurant (reservations required for dinner- closed on Mondays). My favorite gelato and granita was found at Gusto Gelateria, yum!
I didn't have a car but visited Noto as a day trip via bus. I'd considered visiting Ragusa too, but loved Ortigia so much that I stayed there instead.
If you're interested in visiting Villa Romana del Casale, I'd suggest staying in Piazza Armerina.
I stayed at this great B&B, Dimora del Conte, with lovely hosts. My room was the "Room del Conte", it was very spacious with a comfortable bed, sitting area and small balcony with a nice view of the town.
In Agrigento I stayed at this charming b&b, B&B PortAtenea in the historic center. The delicious breakfast was served on the roof terrace where one can see the Valley of the Temples in the far distance. Lovely host too!
My guidebook was the 'Sicily Lonely Planet'.
Sicily is amazing, have a wonderful trip!