Neos Marmaras can be reached by flights to Thessaloniki (SKG) airport. 
From there you can use local bus or taxi to Chalkidiki KTEL bus terminal. There are several buses from Thessaloniki to Neos Marmaras during Summer time. You 
can find more details and timetables here (http://www.ktel-chalkidikis.gr/index1.php). 
You can also hire a taxi from the airport to Neos Marmaras. (Prices aprox.120-150euro)
Alternatively you can hire a car directly in the airport and reach Neos Marmaras within 1-1,5 hours (110km)