Early morning or late day, so you don't bother the beach goers. Do not expect to find much in the way of gold, these are mostly families that go to the beach and they leave their gold at home. Hammonassett Beach, the sand is very soft and stony at low tide and is difficult to dig even with a stainless steel scoop, East Beach and Meigs Point is a little better than West Beach, they have just moved a lot of sand to fill in at West Beach because it washes away during the winter storms. Rocky Neck, is ok but every time a train goes by your detector will go haywire from the electricity. Silver Sands is a long hike to get to and Sherwood Island has a lot of junk in the sand.
Good luck and cover your holes!