Siracusa

Take a day trip to Ragusa, Modica, or Noto (or even the smaller Avola or Scicli) - wonderful Baroque cities to see within 1-2 hours away by train or bus. In Siracusa, see the Archeological Park, Paolo Orsi Museum (amazing if you're interested in archeology), and walk around the small streets in Ortygia (the old part of Siracusa).

Agnes has pretty much covered it!

Those are the same I would have recommended.

Ortigia is lovely, I was there last April. It's a beautiful place to meander, but also has a number of lovely churches to visit. Sitting on the Piazza del Duomo and having an apertivo was wonderful. It is especially beautiful after dark when the entire piazza is flooded with atmospheric lighting.

But when I visited the Archaeological Park in Siracusa, I was very disappointed. The Roman Amphitheater was closed entirely and the Greek Theater was covered in board seating in preparation for the upcoming performances. Had I known that in advance I would not have wasted my time or euros. There are other areas to see in the Park, but for me the two places I mentioned were my primary reasons for going there. You might want to ask about these before handing over your money, that is if they are important to you.

Have a great trip!

Christine is right. I was really bummed to see the entire Roman section closed off with no warning whatsoever when I bought the ticket. It was worthwhile to see the Greek Theater and Ear of Dionysius and quarry section (called latomie). The day I went, the theater was completely unobstructed and the lighting was quite good for photographs. The Paolo Orsi Archeological Museum (around 15 minute walk in the opposite direction) is part of the combined Archeological Park/Museum pass you can buy for 13 Euros (it was cash only at the museum), and it was simply the most amazing, comprehensive collection I've seen in a long time. World class museum worth seeing if you're interested in the area's archeology and Greek and Roman roots.