The most popular public beach in the east end is Coki Point Beach, next to Coral World [1]. Neither too big or too small, Coki has fluffy white sand and a moderate amount of shade. There is good snorkeling just offshore, and a local dive shop rents gear and offers scuba lessons and rentals. There is also an array of beach vendors selling snacks, trinkets, cold drinks, and, if you look carefully, marijuana. The beach gets crowded with residents on weekends and with tourists when a cruise ship is in town.
To find Coki Point Beach, look for signs to Coral World [1] on Route 38 (Smith Bay Road) and take the short, potholed road to the beach. Parking is haphazard and unsecured; leave your valuables at the hotel.
Links:
[1] http://www.moon.com/destinations/virgin-islands/st-thomas/sights/red-hook-and-the-east-end/coral-world