It's about a 45 minute drive from the Savannah airport depending on the time of day. I would take the cross island toll road ($1.25 toll) as it cuts out LOTS of traffic and stop lights while only adding a mile or two distance.
The resort provides a shuttle to the beach much of the day and there is a free Dunes Buggy that runs from 8am - 9pm daily from April - October to cover the times when the resort shuttle does not run.
Enjoy!