Other than some action around the pier, the surfing is poor on Tybee Island [1], with its broad shelf, tepid wave action, and lethal rip currents. But board surfers and kiteboarders have a lot of fun on the south end of Tybee beginning at about 17th Street. The craziest surf is past the rock jetty, but be advised that the rip currents are especially treacherous there.
The best—and pretty much only—surf shop in town is High Tides Surf Shop (405 Hwy. 80, 912/786-6556, www.hightidesurfshop.com [2]). You can get a good local surf report and forecasts at their website.
Links:
[1] http://www.moon.com/destinations/charleston-savannah/savannah/sights/tybee-island
[2] http://www.hightidesurfshop.com