Hitting the Beach -- Near the center of town are two beaches known locally as the Buccaneer Public Beaches; they're adjacent to the Buccaneer Club, on the sheltered western edge of the island, facing Exuma Sound. Snorkeling is good here -- it's best at the point where the pale turquoise waters near the coast deepen to a dark blue. Underwater rocks shelter lots of marine flora and fauna. The waves at these beaches are relatively calm.
On Eleuthera's Atlantic (eastern) side, about 1km (2/3 mile) from Governor's Harbour, is a much longer stretch of mostly pale pink sand, similar to what you'll find in Harbour Island. Known locally as the Club Med Public Beach, it's good for bodysurfing and, on days when storms are surging in the Atlantic, even conventional surfing.
Don't expect any touristy kiosks selling drinks, snacks, or souvenirs at any of these beaches because everything is very pristine and undeveloped.