Our trip to Sicily in September of 2021 budgeted time only for Ortigia, the historic nucleus of Syracuse that has been continuously inhabited for over 3,000 years. The island is very walkable and reasonably compact, high on the historic-feel quotient with a non-trivial measure of decay and lack of TLC, and decidedly short on killer features.

The walk around town will bring you to the Temple of Apollo ruins, the Ortigia street market, the natural spring of Arethusa, the 13th-century Maniace military fort, and other easy on the eye perspectives. Views over the water on the southeastern edge of Ortigia, where the crescent of Lungomare d'Ortigia leaves room for a sliver of a beach are my favorite. Piazza del Duomo is by far the widest public space on the island, presided over by the cathedral that incorporates in its structure the remnants of the Greek Doric Temple of Athena, built on this same site all the way back in the 5th century BCE.

There are also many examples of Baroque both at churches and in civic architecture. (Syracuse happens to be geographically closer to Noto and Ragusa than Catania is, so obviously some rebuilding after the earthquake of 1693 for which "Baroque Towns of Val di Noto" are celebrated occurred here as well.)

We spent over half a day in Ortigia, which is the least it deserves. Several museums - none that I believe are of "must-see" variety - could be worked into the itinerary for a longer stay. The large Parcheggio Molo Sant'antonio is a convenient place to leave the car, less than 5 minutes walk to the bridges that connect Ortigia with the "mainland".

I assume that going to the Neapolis archaeological park is similar in experience to visiting Agrigento, which means at least 2-3 hours. Necropolis of Pantalica is sufficiently far out of the city that I cannot imagine you would prioritize visiting it unless your time in Sicily was not constrained.