Ortygia was by far my favorite place in Sicily: much friendlier than Palermo and much less touristy than Taormina. If fact, it's one of my favorite places ever.
Once again, if you're unfamiliar with driving in Italy, beware: navigating the island is terrifying.
I loved staying at Approdo delle Sirene. The owner is sweet, the location is ideal, and the decor charming (plus you can't beat having your own personal netbook).
You are obligated to visit the Parco Archeologico if you go to Siracusa. I liked it -didn't think it was great - but would have kicked myself if I had missed it.
And as long as you're in the area, check-out the Santuario della Madonna: the contemporary, geometric design was a welcome departure from the multitudes of duomos.
Speaking of duomos, don't miss the Piazza del Duomo and surrounding buildings. I enjoyed perching on the steps and eating my weight in pistachio gelato while people-watching.
If you're in Ortygia on a Saturday, be sure to visit the market in the morning while everything is fresh.
Visit Noto: it's only about a one-hour drive away. Quaint town, interesting architecture.
My big regret was not eating at Il Duomo in Ragusa, approximately two hours from Siracusa. I was just too frazzled from the crazy driving to take on a four-hour adventure. It's the only two Michelin star rated restaurant in Sicily, and obviously the best. I'm truly an idiot for canceling my reservation.
Approdo delle Sirene B&B:
www.apprododellesirene.com/
Parco Archeologico:
www.parcoarcheologico.com/
(the site is under construction)
Il Duomo
www.ristoranteduomo.it/