Many people visit one or more of the Baroque towns (Ragusa, Noto, Modica, Scicli) while staying in Ortygia/Siracusa. They are all very attractive. I think you'll find the public-transportation links are from Siracusa. There are trains and buses linking Catania and Siracusa, but starting the day in Catania would add considerable transportation time. I was able to visit all the towns I listed by using a combination of trains and buses, but I did not see them all on one day.
For car service to the Baroque towns, I'd expect the cost to be higher from Catania.
You may find tours to some of the Baroque towns from Siracusa or possibly from Catania. If they exist, a bit of Googling should uncover them. Try to book directly with the tour operator; that will bring financial benefits to either you or the tour operator, or perhaps both. If you end up on a tour listing on the third-party Viator tour website, scroll down to "Additional Info" and you should find the name of the company actually operating the tour. Most of the time you can find its website via Google.