Agriturismo suggestions for Siracusa, Sicily?

I can't recommend an Agriturismo for Siracusa but we will be returning to Ortigia in the fall for the second time. We will once again be staying at La Via Della Giudecca. We highly recommend this charming B&B. Quiet location, walking distance to sights and restaurants. laviadellagiudecca.it We book directly with the B&B.

Edited to add- if you are looking for other accommodations in Palermo, Agrigento or Catania let me know.

I am not sure how there could be an agriturismo in Siracusa since it is a city — and an agriturismo is a farm

There are some agriturismi kind of close to Siracusa, but they would involve a drive into town, with its accompanying headaches. If you're looking for the experience, why not try Agrigento? Take a look at https://www.agriturismo.it/en/

Unless your flight is very early, you can stay in Taormina the night before. There is direct bus service from Taormina right to Catania airport; you don't have to go into Catania itself or change buses.