I have found a reasonably priced shuttle bus service from Izmir Adnan Menderes airport to Cesme with excellent service. They can drop you off at any hotel in Cesme or in my case at the port for ferry service to Chios, GR. I used them last year and planning to this year.
0232 712 0987
I don't think the web site has been updated for English but call or email Simay and she will accommodate you. She can also setup ferry service or make hotel arrangements.
Last year it was about 20-25 Euro, not sure this year but it beats the 90 Euro taxi fare.