Catania itself is uninteresting but the surroundings are very good. Apart from Taormina/Siracusa I recommend>Aci Trezza/Aci castello
Small town with a medieval castle you can visit and bathe right under, from Aci Trezza you can take a boat and spend the day sunbathing at the Cyclops Rocks, the last piece of land before the open sea>Plemmirio natural reserve
A stunning and less known natural reserve, there are several accesses, just pick one and go down the paths to the sea. It's the southernmost point of the island, you can see Africa on a clear day from there>Fiumefreddo
Pebble beach. The water is immediately deep as fuck as soon as you take five steps from the water line. You can sit on the edge of a literal abyss. I found little pebbles in my stuff for years after going there>Hiking up Mount Etna
Aka motherfucking active volcano. If you don't want to hire a local guide for a tour (there are various lengths and difficulties, renting the proper equipment you can even be taken to the caldera and glance at one of the craters - Etna is a stratovolcano and has several different mouths that open from time to time) you can just walk through the woods at the base up to the Schiena dell'Asino ledge where you can take a good look at the tip of the mountain above and the dry lava bed below (Valle del Bove). Bring sturdy shoes in all cases, cannot stress this enough. Volcano rock is sharp as fuck, my buddy had to use his shoelaces to tie together the pieces of his shoes.