Sicily is one of the most interesting places in the world. After going there the first time, I read an entire book just on its history.A dozen or so empties that have conquered it. Its been a melting pot of these empires. There are particularly strong influences of Greeks, Arabs, and Normans. And these cultures merged and continued. Then the fresh food and produce. Also there is the WWII history. Famously General George Patton swept along the north, and Monty came up through Siracusa and they met in Messina I believe.
In Taormina, both times I stayed, I had a place with a patio and beautiful ocean view and view of Mt Etna. Its seems you kinda get a sunrise and sunset that were both beautiful. The waves are small and you are up high, so you just hear this subtle shimmering sound. Its magical.
they have the Ancient Greek theatre. A path down to the ocean with a cute tiny island, and we were able to walk to the island with shorts on (water maybe 2 feet deep). Then we paid a few euros and took a tram back to the city. The next day, we hiked up from Taormina to a little shrine built into a rock that is hundreds of years old, then we realized there is a whole other town further up another hill. That place is like a city in the clouds. The have remodeled it and have terrace with a wonderful view of the ocean.
Regarding Siracusa, you will appreciate the city more if you read a little about the greatest mathematical of the ancient age, Archimedes who essentially invented calculus 1500 years before Newton, but it was lost and had to be rediscovered. The Romans besieged the city and Archimedes famously had various inventions to fend off the Romans. There are some Myth-Buster videos that seek to verify if he could really set fire to a ship using a parabolic mirror for example. Centuries later, some famous Romans came to Siracusa to find Archimedes grave. There is sculpture tribute in the Main Street of the real city a few blocks from the train station, and there is a museum, but it was a little suspect since they would only take cash. You can pretty much walk the perimeter of Ortygia with great sea views. There are numerous good restaurants that feature excellent fish.
Catania : I have mixed feelings about it. On arrival it looked a bit bombed out and dangerous. But then a few blocks away it was very lively with shopping. Interesting that there is a Catholic Church and a Greek Orthodox Church across the street from it - each with their own styles and designs. There is a great walking tour an hour long on YT which showed some nice places I did not see.
Rome : We actually saw most of the attractions of Rome in a single day of long walking ... hotel near the crime zone of Roma Termini ... Coliseum ... (impossible to get into the old city of Rome booked for the day)... the Mussolini fascist monument which was pretty impressive including the Roman ruins next to it ... Spanish steps ... the Pantheon but did not go in because of the long line. Back to our hotel passing a few working girls out on a cold windy night. A weird thing about the restaurants in Rome. There were three in a close area. Two of them were pretty good. The guy in the 3rd one was very friendly, so we went in, despite there to being many customers. It ended up being 90 minutes of waiting for some pretty bad food.