Just a quick update.
I visited both Hotel Timeo and Sant'andrea. Both are fabulous hotels.
Both being booked, I reluctantly booked 2 nights at Hotel el Jebel. It's the #4 rated hotel for Taormina on TripAdvisor.
It was fantastic. Fantastic as in...one of the top 10 hotels I've ever stayed at. Small - 10-15 rooms I think - but the rooms are well appointed, luxurious, with all the bells and whistles. It's almost like a BnB feel at a full service hotel.
I'd stay there again without a doubt.
No luxury options in Catania, unfortunately. Hotel UNA Palace was as close as you'll get. More like a 4 star hotel. Rooftop terrace and balcony views are a 10/10 though.
EDIT: Hotel el Jebel has it's own private beach with a free shuttle to/from the beach. Having stayed at Sant'andrea's beach, HeJ is far and away the best beach in the area.
Take a boat ride to the caves around Taormina if you have a chance. If anyone is interested, I'll post some pictures.