Cesme is an international sea-side resort on the Aegean.
There are several ways to get to Cesme, it's an half an hour drive from Izmir by car, and there are several bus companies that will drive you to Cesme from Izmir on any time of the day. Buses from Cesme to Izmir at the time of writing are around YTL 10, ie around EUR 5.
There is one, possibly two, daily ferry(ies) to Cesme from the Greek island of Chios, the boat ride takes slightly over an hour and costs the whopping sum (for such a short ride) of 23 euros.
Bus services are also available from Istanbul, the route lasts approximately 8 hours.