Forecasters were predicting the storm would pass through Georgia overnight, and the island would likely re-open to tourists Friday.
"It looks like it's picking up speed and that's a good thing because it won't sit and rain on us so long," said Jan Chamberlain, whose family runs the Blue Heron Inn Bed & Breakfast near the Sapelo Island Ferry station on Georgia's coast, on Thursday.
In the Carolinas, Andrea's biggest threat was heavy rain, with as much as 6 inches expected, the weather service said.
Forecasters didn't expect major problems, however, along the most vulnerable parts of the coast such as the Outer Banks, a popular tourist destination.
John Elardo, a meteorologist with the weather service in Newport, N.C., said the storm would push major waves to the north and northeast, away from the Outer Banks, where storms in the fall and winter wore away dunes and washed out portions of N.C. Highway 12, the only road connecting the barrier island to the mainland of North Carolina.
Andrea could bring up to a foot of flooding on the sound side of the Outer Banks, Elardo said.
The rain threatened to ruin a beach day for Angela Hursh, 41, of Cincinnati, who had rented a house in Frisco, N.C. Hursh was planning Friday to soak in the hot tub and watch movies with her 9-year-old and 13-year-old daughters.
"I think we're just going to hunker down and eat junk food," Hursh said Thursday.
Doug Brindley, who owns a vacation lodging rental service on the northern end of the Outer Banks near Virginia, said Thursday he expects all outdoor activities to be washed out Friday, driving tens of thousands of early-summer vacationers toward unexpected shopping sprees.
"We're going to have rain and wind," said Brindley, who owns Brindley Beach Vacations and Sales. "Retailers are going to love it."
In Cuba, heavy rains associated with the storm system have soaked the western part of the island for the past several days, overflowing rivers and damaging crops. At least 30 towns were cut off by flooding, and more than 2,600 people sought refuge from the rising waters at relatives' homes or state-run shelters, the Communist Party newspaper Granma reported Thursday.
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Contributing to this report were Associated Press writers Jeff Martin in Atlanta; Russ Bynum in Savannah, Ga.; Gary Fineout and Brent Kallestad in Tallahassee, Fla.; Peter Orsi in Havana; and Emery P. Dalesio in Raleigh, N.C.