Sicily

Excellent Plan! Daytrips out of Siracusa by bus or train: 1. Allow two full days for Siracusa (one for Ortygia Island, the other for the adjacent mainland) 2. Noto (can be one-half day, together with Modica) 3. Modica 4. Ragusa 5. Palazzolo Acreide 6. Catania 7. Taormina This amounts to 7 days! www.interbus.it (CTA to Siracusa; Siracusa to Catania; Catania to Taormina; Taormina train station to central Taormina) www.aziendasicilianatrasporti.it (Siracusa to: Noto, Modica, Ragusa, Palazzolo Acreide)
www.ferroviedellostato.it (Siracusa to: Noto, Modica, Ragusa, Catania, Taormina)

I don't know how to advise you about bus or train (we did it by car), but when in Sicily you should somehow find a way to visit the extraordinary UNESCO World Heritage sites of Agrigento (the Valley of the Temples) and the Villa Romana del Casale, near Piazza Armerina. Also the magnificent Greek temple & hilltop amphitheater at Segesta. All of these should be particularly beautiful in the month of May.

Using public transport, neither Agrigento nor Piazza Armerina (Roma Villa at Casale) would be suitable for daytrips out of Siracusa. You would need to spend one night in either place. Here's how to get to each of these places: 1. Siracusa to Agrigento: Best solution is to take the Interbus bus service to Catania Airport, then connect to the SAIS Trasporti bus to Agrigento. Another solution (from Ragusa) is to take the A.S.T. bus or the Trenitalia train to Gela, then connect to the S.A.L. bus to Agrigento (NOT on Sundays) 2. Siracusa to Piazza Armerina: Two choices here: (i) direct A.S.T. bus to Piazza Armerina (4 hours); or (ii) Interbus bus to Catania Airport, then connect to Interbus bus to Piazza Armerina. 3. Piazza Armerina to Agrigento Two choices here: (i) take the Astra Bus to Gela, then the S.A.L. bus to Agigento; or (ii) take the Astra Bus to Caltanisetta, then the SAIS Trasporti bus to Agrigento www.interbus.it www.aziendasicilianatrasporti.it www.saistrasporti.it www.autolineesal.it
www.ferroviedellostato.it See also: http://www.fodors.com/community/europe/piazza-armerina-to-and-from-agrigento.cfm

Thanks everyone for all of the information. It will be a great help.

You could visit the Valley of the Temples and Mount Etna by excursion or private transfer. http://www.easternsicilyguides.com/itineraries.html
http://www.sicily-tour.com/