I know that in Italy prices do not always correspond with the number of official stars.... I would say that around 200 Euros per night/per room would be OK. If we can find something lovely for a lesser price, this is even better.
Also a swimming-pool, or access to nearby beach would be great!
Regarding Syracusa, I have read that it was better to stay in Ortigia, but in terms of quietness, a place on the mainland could be better... Visiting the temples is of course on our list!
Many thanks for your feedback.