Ah, super. You should be able to cover quite a bit of ground in 2 weeks, so 2 locations sounds ideal.
If looking for a contrast and to cut down on car hire duration, one of those weeks could be on the Aeolian islands, allowing the regular ferries and occasional excursion (e.g. night boat to see the natural fireworks of Stromboli) to offer easy day trips. Salina or Lipari are the easiest choices of base island. The ferries go from Milazzo, which could work nicely if driving or taking the train to Sicily. There's also a ferry from Palermo if you end up flying into (or out of) that city.
Others will have better insight on the 'mainland', but options might include a road trip along the south agrigento, ragusa, siracusa, modica, noto etc., exploring Etna's wines and landscape, immersing in the two vibrant (but perhaps a bit too intense for our tastes) cities of Catania and Palermo. Maybe a bit early in the season for Taormina? I'm sure there's 2 weeks worth on the mainland if the islands don't appeal.