Some airports, government buildings, schools and the New York Stock Exchange are due to return to business.
But many homes still have no power and the New York subway will remain shut. More than 40 people are dead.
President Barack Obama, who has suspended his election campaign, is due to visit affected areas in New Jersey.
The cost of clearing up after storm Sandy has been estimated at $30-40 billion.
New York Governor Andrew Cuomo said: “We have not seen damage like this in a generation.”
The storm is still causing severe disruption after moving inland from the coast. It is forecast to weaken as it turns north into Canada, but to continue dumping heavy snow and rainfall.
At least 22 people were killed in New York City alone.
JFK and Newark Liberty – two of the New York area’s three main airports – were scheduled to open for a limited service on Wednesday, but severe delays were expected after the cancellation of more than 18,000 flights across the affected area.
The New York Stock Exchange says it will also re-open after two days’ closure, as will the Nasdaq exchange. The last time the stock exchange shut down for two days was in 1888.
New York’s subway system sustained the worst damage in its 108-year history, said Joseph Lhota, head of the Metropolitan Transit Authority (MTA).
Subway tunnels were flooded and electrical equipment will have to be cleaned before the network can re-open.
New York Mayor Michael Bloomberg said there was “no timeline” for when the subway would restart, but he hoped buses could begin running again on Wednesday.
Trams and ferries were resuming services, but most of New York’s bridges remain closed.
Across the north-east, at least eight million homes and businesses are without power because of the storm, says the US Department of Energy.
Sandy brought a record storm surge of almost 14 ft (4.2 m) to central Manhattan, well above the previous record of 10 ft during Hurricane Donna in 1960, the National Weather Service said.
Maryland appeared to have the worst of the rain and snow – with falls of 12.5 in (32 cm) and 28 in respectively.
President Barack Obama was due to tour disaster areas in New Jersey on Wednesday with New Jersey Governor Chris Christie.
Chris Christie, a Republican and staunch supporter of Mitt Romney, went out of his way to praise the Democratic president for his handling of the storm.
“I spoke to the president three times yesterday,” Chris Christie told CNN.
“He’s been incredibly supportive and helpful to our state and not once did he bring up the election… If he’s not bringing it up, I’m certainly not going to bring it up.”
Mitt Romney resumed low-key campaigning on Tuesday, converting a rally into a storm relief event in the swing state of Ohio.
In other developments:
• US federal agencies in Washington DC will re-open on Wednesday
• Fire destroyed about 50 homes in the New York City borough of Queens
• More than 200 patients were evacuated from New York University’s Tisch Hospital after power went out and a backup generator failed
• Three nuclear reactors have been closed due to electrical supply and cooling system problems; a fourth was put on alert because of rising water.
In all, storm Sandy has claimed well over 100 lives, after killing nearly 70 people as it hit the Caribbean.
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