Better to stay outside of Ortigia (less pricey). Some ideas are: Giuggiulena, Musciara in Siracusa by the sea and walking distance to Ortigia. In the countryside, there is Villa dei Papiri, 8km to Ortigia. At the seaside: White Bay. In the heart of Syracuse, on Ortigia, the Domus Mariae Benessere. It is owned and managed by the order of Catholic Nuns.