Hi Erin,
Here's what I did in 4 full and (regrettably) busy days, since I went to Sicily as a side trip from Malta. I concentrated only on the southeastern part (the USESCO Baroque cities). Flew into Catania in the early AM, took the earliest 8:00am ish bus to Siracusa (~ 2 hours, no traffic on the road) and spent the rest of the day just in the archeological park (Greek and Roman theaters) and excellent Paolo Orsi Archeological Museum (could have spent and entire day or two just in the museum alone, no joke. It is huge, very time-intensive, and very comprehensive). Second day was spent 1/2 day walking around Ortygia (old city of Siracusa) and 1 hour bus trip to Noto (another lovely Baroque city very close by) for the afternoon to evening. Returned to Siracusa in late evening and spent the night. Allocated one full day for day trip to Ragusa, which was a very long day (I LOVED Ragusa - would have wanted to spend more time there and stay overnight but it was Ok for a day trip, albeit a very long one). The train took 2 hours or so to get there. Then on the last day, took bus to Taormina in the early AM, spent the day there (~7 hours or so) and then took the bus back to Catania Airport for a 10:00 pm flight back to Malta. So, for the whole 4 days, I used Siracusa as the base and took side trips to Noto, Ragusa, and Taormina before circling back to Catania. If you're short on time, you can visit Modica as a substitute for Ragusa - also a fascinating city I never got to because 4 days was not enough time. Tons of UNESCO sites there as well.
I would say based on my experience that Taormina deserved the least amount of time (full day is fine) and Siracusa deserved at least 2 full days (assuming you want to see the archeological treasures, which I think shouldn't be missed) and 2 days for Ragusa (there is a lot of walking and if you want to take your time and really enjoy it, a day trip will seem too short). Noto was fine for a 1/2 day because it was very compact. So that's why I say "avoid the rush" if you can - you'll have a better experience if you see less cities but for longer. My favorite by far was Ragusa because it was terrific to take a long walk from the new town down to the old town below and just wander around - there are wayyyy too many UNESCO sites (mostly churches and palazzos) to see there.