I really recommend walking around the old town, the heart of Syracuse, early morning before the tourist woke up. Have a cup of coffee and just enjoy the  wings of history. Don't forget to visit the Catedral as well. 

It is really fascinating to see all the houses that were built once upon a time. Narrow streets that leads  you through a "historical landscape" of culture and architecture. The most interesting thing is the history of Lucia. For a second I thought I found her. But, she turned out not to be from Italy at all, but from the south of France :)