Rental car and parking on Ortygia

There is a parking lot on the edge of the island. Actually there are several, but the one I used was called Parcheggio Talete and is on the far northeast side of the island. It's an easy walk to anywhere in Ortygia (only a mile to what looks like the farthest point at Castello Maniace and your hotel will likely be much closer) , but with luggage you may be able to drive to the hotel, drop off luggage, then park in the lot and walk. The driving restrictions are only at certain times.

There is also a circulator bus that goes around the island if you prefer that.

At the lot you park your car, leave, and then when you return you pay at a machine by entering your license plate number. Cars are tracked by camera entering so they know the times.

I would stay on Ortygia if possible - it is the most charming and pleasant area for walking around at night.

This website helped me with driving and parking:
http://www.reidsitaly.com/destinations/sicily/southeast_sicily/siracusa/planning/get-around.html

Ortigia is an excellent base. Our favorite place in Sicily. We highly recommend the accomodations at La Via della Giudecca B & B (Via Della Alla Giudecca 4). We had a large apartment with a patio and lovely view. Charming, comfortable and convenient short walk to the Duomo, historic center, restaurants and daily market. The town is absolutely magical at night! We would not hesitate to stay there again. Not familiar with the parking there since we took the train.

Thank you for your replies.

We got a parking ticket for overnigh parking in Ortigis and then found out about the public car park, unattended during the day, but attended at night. Our B&B host very sweetly insisted on paying for part of the fine, which we paid at the post office nearby.