Siracusa was once bigger than Athens, richer than Corinth. Cicero called it "the greatest Greek city." 1 hour from Catania, Ortygia island alone is worth the trip.
Catania Centrale → Siracusa. Direct. Station is 15 min walk from Ortygia across the bridge.
Drops you closer to Ortygia.
Train, 1 hour. The most important ancient Greek site in Italy. Give it a full day minimum.