To get around Siracusa, you can walk from site to site or use public transportation. There are buses that run between the sites and taxis are also available. A taxi from the train station to your first destination, the Ancient Greek Theater, will cost around €10 and take about 10 minutes.
If you have more time, consider visiting other nearby attractions such as the Catacombs of San Giovanni and the Maniace Castle. If you have less time, you might skip the Ear of Dionysius or Ortygia Island and spend more time at the other two locations.