I love Sicily. We're going in mid April. I have no reccomendations for a villa with a pool, since we usually rent small apartments via VRBO or Airbnb. My husband has family in the Catania area - with the largest cluster in Riposto/Giarre area.
If having a pool isn't a dealbreaker I can highly recommend the apartments at Residence Schuler.
https://www.residenceschuler.com/en/
The owner is the brother of the local hotel "Villa Schuler" (which may have a pool, don't know). The apartments are very nice and have amazing views. It's very walkable to Corso Umberto for your evening passiagiata.
Again no pool, but closer to Etna is Nake Residenzia - disclaimer, this is owned and operated by my husband's 2nd cousins. It's a beautiful home in San'Alfio with the most amazing views of both Etna and the sea. Nilla, who runs it, speaks perfect english and can help arrange things for you. A car is required because it's in a small town not well serviced by train or bus.
https://www.nakesicily.it/index.php?l=en
Things to do or see if you are based in the Catania area:
- Siracusa: explore both the old island of Ortygia and the Greek stadium and ruins nearby.
- Taormina: Up the hill from the ocean, but you can take a tram down to the water. Beautiful town, beautiful greek arena. If you are a walker hike up/back to Castelmola. Or take the bus or a taxi to Castelmola and walk down to Taormina.
- Piazza Amerina/Villa del Casale - Amazing mosaics. Can be combined as a day trip to Caltigirone.
- Catligirone: The most beautiful ceramics. And the risers on the steps up to the church are all beautifully tiles. Ceramics sold from Caltigirone has a special cache - make sure it is marked Caltigirone. (Some of our favorite serving bowls are from here.
- Agrigento - one of the best sites for Greek temples. (Full day trip to get there and back from Catania area).
We also enjoyed taking the circumferovia train that circles (most of the way) around Etna. It starts in either Catania or Giarre/Riposto - so you have to take a regional train to close the loop...
For Etna there is a Gondola that takes you close to the top, then you can take a tour out. We went in late June and there was still snow and it was super windy - so definitely bring a warm jacket.
On the other side of the island we based in Marsala and enjoyed the Trapani salt flats, the town of Erice (stunning!!!) and trips to Palermo and Monreale (the cathedral has some of the best mosaic 'frescos' I've ever seen.) We rented a guest house just outside Marsala and had shared use of the family pool.