Sicily towns

Haven’t been to Ragusa, but other than the Valley of the Temples, there’s little else in Agrigento. The temples will only take a half day at most to see. We spent 3 hours at the temples. We stayed two nights at B&B Villa San Marcos and walked to the temples from it. It’s a half mile down a dirt road so without a car, you’d need to take a taxi to reach it.

Having been to both, if you choose 1, it should be Agrigento.

The previous poster was right. There's very little in Agrigento other than the ruins but I would add the Sal 8 restaurant, which was great. The town walk was so boring we abandoned it mid-way. If your itinerary would permit it, I'd recommend Selinunte and/or Segesta over Agrigento. Both are much less crowded and more enjoyable. Segesta has a much better on-site explanation (using large bilingual displays) for each site in the park. We really liked Ragusa. It's small, but very pleasant. The walk from Superiore to Ibla is fun (and much better than going uphill). The other must-see for me at least was Cinabro Carrettiere. For a mere 10 euro you get a private tour and lots of interesting conversation on the process of making and marketing the traditional Sicilian carts. I you keep a fairly quick pace, Ragusa can be accomplished in 1-1.5 days. But, it was a good place, too, for a couple of down days. It's a bit of a schlep (like 1.5 hours), but if you're going to be there 3 nights, and have a car, I'd consider going to Villa Romana del Casale. I'm not sure what public transportation options would be available, but it's easily reachable by car. All things considered, I'd vote for Ragusa.

I have been to all of these and Ragusa, Modica, Palermo, Siracusa, etc.

YES
Cefalu Yes - definitely. Cefalu has a bit of a walk to the main area. Great food - including some local cuisine. Many shops but not overly touristy. A nice long sandy beach and the monolithic mountain behind it (which offers some hiking)
Taormina Yes - definitely. Taormina is way up on a hill. You can pay 20 eu for a taxi or just wait 15 minutes and pay 1 eu to go up. Breathtaking views if you get a hotel with a view (as we did each of many times there). There are some good restaurants but also some over priced tourist restaurants. A great hike down to the water and the tiny island, or alternatively a great hike up to the chapel above the city. Definitely full of tourists only and essentially few locals. Also Greek theatre.

NO
Messina is probably a place to be avoided. Its the only time in Italy where I saw 3 armed police walking the train station and hassling people that looked like they did not belong

MAYBE
Catania - during daylight hours in the city center there is a fine open air market which is colorful and full of good food. The city's Main Street is good but not great. Some of the areas near the train station seem dangerous - graffiti, deserted buildings, etc.
Ragusa - it's a good place. You arrive in the newer city which is kind of one one giant hill, then you walk over, and across a small valley is the old city. So thats where you get the iconic photos. The old city itself is pleasant but not amazing. I am not sure it's that great of a place to visit though. No matter if you arrive by bus or train, you have a long walk to the city center for the new city, much less the old city. there were no trams or subways. there were buses which did not seem to maintain any kind of schedule (verified by hotel staff). I ended up walking 30,000 steps one day there.
Modica" - near Ragusa is Modica - a big hill town, a lot of walking. A very nice church from 1600's near top of hill, similar to ones we saw in Ragusa. We saw them selling the local chocolate bars but no chocolate tasting or theme parks like Hershey, Pennsylvania. We wouldn't go back.
**Scicli - also near Ragusa - we liked this smaller flatter place a bit better than Modica

ALSO YES
Noto - an hour from Siracusa or Ragusa, I liked this little town. Had some great food, and the architecture seemed more organize and consistent.
Siracusa - I really like this place, great food, a great fish market, a variety of nice ocean views and sea walls, medieval streets, and several Greek ruins.
Palermo - This is the capitol, has the UNESCO Norman churches which are stunning, a big vibrant city with some nice sights, and not one, but three separate open air markets. We had some great food there. If you read the history of Sicily, this was the seat of the Norman rulers which merged Greek, Arab, and French culture harmoniously.