Sicily in 3 Days

You only have 3 days which is very little, so it's best to minimize your travel time. Take a short flight into Catania and make that your base. It's somewhat equidistant between Siracusa and Taormina, so you can take two day trips (on separate days because one city is ~ 2 hours to the north and the other is ~ 2 hours to the south of Catania) and spend the last day in Catania before your flight. Do you truly have 3 "full" days to begin with?

Alternatively, you can make Siracusa your base. But in this case, it will not be as convenient to see Taormina unless you're prepared to spend the night there. I think two bases in three days is a bit much, but it's up to you. If you choose Siracusa, I would strike Taormina and replace with Noto, which is only an hour away and is very lovely. You can easily spend all three days in Siracusa as well. I've been to Taormina and, frankly, one day was totally adequate (I saw pretty much everything in that one day).

You say that you only have three days so that means you have four nights? Is that correct since two nights equals one day? When are you planning to go to Sicily?
With so little time, fly to Catania from Naples.
Stay in either Taormina or Siracusa and day trip( car, bus, train, driver) to the other location. I would choose Siracusa and stay on Ortigia Island.
Sicily is quite large so three days barely gives you enough time to see one location.

I agree with Agnes, best to stay in Catania and daytrip from there.