The storm was blamed for the deaths of 157 people -- at least 88 of them in the United States, two in Canada and 67 in the Caribbean.
The bodies of two children were found Thursday. The boys, ages 2 and 4, had been riding with their mother on Staten Island when the storm surge swamped their SUV, authorities said.
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They were found Thursday morning "maybe a block or two from where (their mother) lost them," Borough President James Molinaro said.
Boats were beached on front yards in the Staten Island neighborhood of Great Kills. Several people were missing.
Also on Staten Island, John Filipowicz, 51, and his 20-year-old son, John, were found dead under debris in the basement of their home, which had been swamped by the storm surge, authorities told CNN affiliate WCBS.
Sandy claimed at least 37 lives in New York City, Mayor Michael Bloomberg told reporters Thursday.
That toll included 13-year-old Andrea Dresch, whose body was pulled from the debris of a house on Staten Island that was swallowed by a tidal surge, authorities told WCBS. Her father was among the missing, SILive.com reported.
While some mourned, others focused on the struggle facing the living -- as authorities in nine states worked to restore basic services such as public transit and electricity.
When it comes to electricity, Manhattan has become an island of haves and have-nots. About 530,000 customers were without power citywide, Bloomberg said, many of them south of Midtown's 34th Street. Parts of Queens and Staten Island also had no electricity Thursday. "Restoring power will take a lot of time," the mayor said.
New York's vast transit network remains hobbled. The Metropolitan Transit Authority said 14 of the city's 23 subway lines were running and a flotilla of 4,000 buses was attempting to take up the slack. For some, Thursday's commute into Manhattan from the outer boroughs took five hours.
Bloomberg predicted that would ease, as tunnels are cleared of water, power is restored to subway lines and ferries resume service.
Getting water out of the tunnels is "one of the main orders of business right now," Gov. Andrew Cuomo said.
But Broadway theaters were to reopen Thursday, and organizers vowed to hold the New York City Marathon as scheduled on Sunday. Event organizer Mary Wittenberg said the race wouldn't divert resources from the recovery.
Nearly three days after Sandy came ashore in southern New Jersey, search-and-rescue crews were going door-to-door in some neighborhoods looking for people, particularly the elderly, who may have been stranded by the power outages, the debris and remaining floodwater.
Sandy killed at least six people in New Jersey, said Gov. Chris Christie, who had warned people in low-lying areas to evacuate. "We're lucky that more people didn't die as a result of folks ignoring those warnings," he told reporters on Wednesday.