Galveston County Sheriff Gean Leonard said search teams were combing Bolivar Peninsula, but he had little information by Monday afternoon. The hard-hit area was closed to all but rescue workers.
"We're just getting reports in that Bolivar is to a great extent destroyed," the sheriff said.
As of Monday, no fatalities had been reported.
As of Monday afternoon, about 10,000 of the city's 70,000 residents were without power, City Councilman Jim Nelson said. Water and sewer services were restored.
Overall, the city escaped major damage, but some streets flooded, especially in the Glen Cove and Bayou Brae subdivisions.
City Hall sustained minor damage, with some pieces of granite blown off the side of the building, Nelson said. City Hall was expected to remain closed at least a week, he said.
The city's dawn-to-dusk curfew was lifted early Monday. No arrests for looting were reported, Nelson said.
The city was still without electricity Monday, but crews from power companies were working to restore service.
The city's water services were restored, and there was no need for residents to boil their drinking water, Mayor David Smith said Monday.
A few minor injuries were reported, including the owner of a gasoline station, who was hurt when a customer in a vehicle drove over his foot, Smith said. The owner was treated at the scene.
Trash pickup and debris removal will continue "until we get everything clean," he said. "Folks are going to need to maintain their patience levels, because we have a lot of recovery to do."
Dickinson sustained minimal flooding, but many trees were down and "pretty much everyone is without power," Galveston County Commissioner Stephen Holmes said. Residents are being asked not to return yet.
TEXAS CITY Like La Marque, Texas City had "minimal flooding and lots of debris," Holmes said.
Evacuees who return home should prepare themselves to see an altered landscape, he said.
"Obviously, they need to prepare themselves for what they're going to see visually — trees and debris," he said. "It's kind of overwhelming emotionally. "The amount of debris is just overwhelming."