RS Sicily tour

There are buses and trains to Noto from Ortigia/ Siracusa. Aren’t you including Ragusa?
You could also hire a driver service if you don’t want to rent a car which would be the easiest solution.

I'd recommend heartily against the train from Siracusa to Noto. It is a very long walk uphill from the station to town, and there are no "official" taxis. We hired a guy by flagging him down on the street. Not terrible, but not recommended either.

We based ourselves in Ortigia after our guided tour ended in Taormina. We spent 5 nights. Our BnB host arranged a driver for a day trip to Noto, Modica and Ragusa. We also stopped along the way for other sights. Highly recommend visiting these wonderful Baroque towns. Ortigia was our favorite base. We had planned to return in 2020, but that didn’t happen! Enjoy your planning.

I took buses from Siracusa to those towns, no need for a car. The only thing to watch out for with buses is they don't run on Sundays, or very infrequently (but other days are fine). Many people going to Sicily for the first time assume that trains are better than buses, but they are not only slow and really old in this part of Sicily, they also don't drop you off as close to the town centers as the buses do (for these towns and Taormina too).

We finished the RS tour in early October and took the direct bus from Catania to Noto. The bus stop is adjacent to the park at the SE edge of the old town, easy walking distance to our B&B. After 3 fun, relaxing days in Noto, we had tickets to take the train to Ragusa Ibla, but a personal issue resulted in hiring a taxi (90€) to drive us. I'd say the towns are pretty easy to access by public transport if you are willing to do a bit of walking from the stations to the old towns. We really enjoyed our time there.

Thank you all for the great suggestions. Which town do you think will work best as a base for day trips?