Located near the south-eastern corner of Sicily on the Ionian coast, Siracusa (Syracuse) is built on an ancient Greek settlement founded by Corinthians in 734 BC (BCE). More than any other modern city in Sicily, Syracuse manifests a visible continuity from its ancient Greek past, both historical and mythological. Its older quarter is an island, Ortegia (or Ortygia, from the Greek for "quail," probably named for that bird's abundance in this area). Ortegia is known for, among many other things, the freshwater Spring of Arethusa. When Artemis changed Arethusa into a spring of water to escape the river god Alpheus, it was here that the transformed maiden emerged. On a more factual note, Syracuse was the city of Archimedes, Pindar and Aeschylus. It was the most important city in Magna Graecia, with a population of around 300,000, and for a time rivalled Athens as the most important city of the Greek world. However, it was not the first "Greek" settlement in Sicily.
In the modern day, the city is listed by UNESCO, as a World Heritage Site. Highlights are the Ear of Dionysius, the Greek Theatre (in which each year are the performances classic: tragedy), Fountain of Arethusa, Temple of Apollo, Castello Maniace, many very interesting Church and edifices, and the beautiful Cathedral (that was Temple of Athena): a baroque facade, an early medieval interior, but basically still the Greek structure it was when it was erected as a temple to the Greek Gods.
And yes, there are beaches nearby, and there's no shortage of good restaurants in Syracuse, but we suggest you avoid those that offer "tourist menus" in favour of the charming pizzerias and seafood restaurants. The seafood specialties are seasonal to some extent. The pasta dishes with mussels and urchins are especially tasty but more available in spring and fall than summer.