How many days would you allot to seeing Catania itself? We will be staying also in Syracuse and Taormina...
Of the 13 days I spent in Eastern Sicily (only, Western side will be a separate trip) I spent a day and a half in Catania. That was more than enough to see the basilica, Greek Theater, wander the gardens, have a relaxing dinner and do some last minute shopping for Limoncello :-)
On a shorter trip where you're flying out of Catania, and assuming you've allocated 3 solid days to Siracusa and Ortigia and 1 or 2 to Taormina, I'd plan to arrive late morning and spend the afternoon and evening there before your flight.
Were I to return, I’d stay a minimum of 2 1/2 days and add the fish market, WW II and Cinema museums and schedule a trip to Etna. Enjoy the cannoli and arancini.
The WWII museum — called Museo Storico Dello Sbarco in Sicilia 1943 — was very interesting and worth a couple of hours. The museum tells the story of the landing of the allies in 1943 from the Sicilian perspective. Lots of uniforms, arms and maps — most of which is described in both Italian and English. Fun and informative even if you’re not a military history buff (as I am not).
Have a great trip!
DD