Siracusa owns an old Mediterranean heart in Ortygia, a harbour Venetian or Cretan in its looks. Crumbling buildings, a street market, colourful balconies, drying laundry from the windows: a true delight to the senses. There's nothing else to do than wander the quiet streets, peeking around corners and awe at the ubiquitous churches and palazzi. The attractive and open Piazza Duomo (I found it hard to find at first) has the most prominent buildings.
Like in some of the other places I visited in Sicily there is a lot of reconstruction going on. Ortygia's Duomo is one of the monuments that are under scaffolding at the moment. Don't let this put you off visiting, there's so much more to see. I didn't get into any of the buildings, just roamed around and had a fine time. Siracusa is well on the beaten path for the general tour groups, I noticed even a cruise ship disembarking its passengers here for a visit!
I skipped Neapolis due to an Ancient Greek/Roman overdose I felt coming, but did manage to get to the necropolis of Pantalica. About an hour outside of Siracusa, it can be reached via a scenic road that shows the Sicilian countryside at its best. The drive there on small mountain roads, lined by olive trees and the occasional village (pretty Ferla!) is actually more worth it than the burial site itself. To the untrained eye, the burial chambers that held whole families are merely holes in the rocks.