Siracusa divides naturally into two zones: the island of Ortigia, where the ancient and baroque layers stack up in a remarkably small area, and the mainland Neapolis Archaeological Park, where the Greek theatre, the Roman amphitheatre, and the Ear of Dionysius require a good two hours to see properly. Most visitors spend their time on Ortigia — it is among the most atmospheric old towns in the Mediterranean — but the Neapolis is the more arresting destination historically.
Plan to spend at least two full days: one for Ortigia and the cathedral area, one for the archaeological park and the Museo Paolo Orsi. The Ortigia market, open every morning Monday through Saturday, is the best reason to rise early.