Short answers, pulled from the story.
Syracuse was founded in 733 BC by colonists from Corinth under the leadership of Archias. This group expelled the Sicels, the previous inhabitants of Ortygia, to establish their new colony.
Roman legions entered Syracuse after prolonged resistance and captured the city under consul Marcus Claudius Marcellus. During the conquest, a Roman soldier killed Archimedes and looted all accumulated wealth to transport it to Rome.
Emperor Constans II designated Syracuse as the capital of the Eastern Empire to replace Constantinople during his reign. The emperor died at the Daphne Baths while Syracuse held this status for five years before Arab attacks intensified.
Syracuse endured bombings from 1941 to 1943 including an attack on the liner Conte Rosso that caused over 1,200 deaths. The Allies occupied the city between July 9 and the 10th of July 1943 through Operation Ladbroke and signed the armistice with Italy near Cassibile on the 3rd of September 1943.
Syracuse sits on the southeastern side of Sicily surrounded by the Ionian Sea basin and featuring hills and natural caves. Two rivers named Anapo and Ciane flow along its southwestern edge and merge into a single mouth in the sea near Pantanelli.
UNESCO included Syracuse among World Heritage Sites in 2005 alongside the Necropolis of Pantalica. The Neapolis Archaeological Park covers 240,000 square meters and contains Greek theaters, Roman amphitheaters, the Ear of Dionysius, and twelve groups of necropolises dating from the 8th century BC to the Byzantine era.