Ragusa, Modica or Noto

Definitely Ragusa (it is most similar to Modica in its layout and feel, and they are fairly close together) because of the way it is situated with a higher (newer) and lower (older) town...absolutely stunning to walk down to the lower town (called Ragusa Ibla) and to look down upon it from a series of stairs. It has tons of (UNESCO) sights to see - mostly churches and palazzos - and all are well marked. It was my favorite town of the ones I visited in that region. Noto is beautiful too but it's more compact and level with a relatively short pedestrian main drag and lots of hilly side-streets - it's a lovely Baroque city you can see in a few hours. Ragusa took all day (due to lots of walking) and I was so sad I didn't end up staying longer (but I had to take the last train back to Siracusa). I don't think you can go wrong no matter which you choose because they are all beautiful, but for me, Ragusa was a true standout.

Here are some maps (Noto is missing but it's the most straightforward of the three because Ragusa and Modica are so curvy). They took me a long time to find, so I want to share:
Modica
http://www.pietrenereresort.it/wp-content/uploads/Modica-Historical-Centre.jpg

Ragusa
http://www.comune.ragusa.gov.it/turismo/mappacitta/_allegati/cartina_rg.pdf
http://www.pietrenereresort.it/wp-content/uploads/Ragusa-map.jpg
http://www.comune.ragusa.gov.it/turismo/mappacitta/_allegati/marina.pdf

Agree that Ragusa is the best town to stay. We stayed in Ragusa Ibla and enjoyed walking through the old town, both daytime and night.

Ragusa is lovely and I can highly recommend Quattro Gatti for dinner.

There is a blog site called Baroque Sicily that you may find helpful. The American lady who wrote it lives in Ragusa, in the old part of the town. Her photos are incredible and I think that you would find the site helpful. Unfortunately, she seems to have ended her blog site last Christmas, which is too bad as it was very interesting.