central catania is great, beyond the centre a bit of dump. Syracuse was more like that, nicer centro storico, more of a dump away from it although with a bit more Ancient Rome scattered about. Taormina is ye olde italia theme park (also a total nightmare to drive a van round in) but definitely worth a wander round in. Gets busy though The Greco Roman amphitheatre is a must do and allow plenty of time for it because you’ll need to soak up the view down the coast which will stay with you for a long time.
Catania central at night is pretty cool. The town is built of the lava stone that destroyed the city centuries ago so many buildings are black faced with white on cornerstones and sills making it very gothic. A trip to the top of Etna is the must do thing here.
I’d be looking at at least a day in all 3 probably based in Catania because it’s between Taormina and Syracuse. Trains are excellent and if you fancy a day in Naples, you can overnight on the sleeper (train gets on the ferry to cross the straits of Messina)
I’ll be driving up the coast in a couple of months and wil visit Taormina again but dump the van on the outskirts (IIRC there’s a park & ride between the autostrada and town proper)