Flights have resumed to airports in New York. Some federal offices, schools and Wall Street has reopened.
But many homes still have no power and the New York subway remains shut. More than 40 people are dead.
President Barack Obama, who has put campaigning on hold, is due to visit affected areas in New Jersey.
The cost of clearing up after the storm has been estimated at $30-40bn (£18-24bn).
New York Governor Andrew Cuomo said: "We have not seen damage like this in a generation."
Flight backlog
Republican presidential nominee Mitt Romney is due to campaign in the swing state of Florida, as is Democratic Vice-President Joe Biden.
Meanwhile, Mr Romney's running mate, Paul Ryan has appearances planned in his home state of Wisconsin.
People have begun returning to the homes they abandoned on the orders of local authorities.
"It's heartbreaking after being here 37 years. You see your home demolished like this, it's tough," Barry Prezioso of Point Pleasant, a beachfront community in New Jersey, told the Associated Press.
"But nobody got hurt and the upstairs is still liveable, so we can still live upstairs and clean this out. I'm sure there's people that had worse. I feel kind of lucky."
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.
Flights started arriving at JFK and Newark Liberty airports on Wednesday morning. Services will be limited, and delays are expected after the cancellation of more than 18,000 flights across the affected area. LaGuardia airport remains closed.
New York Mayor Michael Bloomberg rang the opening bell at the New York Stock Exchange on Wednesday, which reopened, along with the Nasdaq, after two days' closure.
The last time the stock exchange shut down for so long because of the weather 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 reopen.
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, and most of New York's bridges have been re-opened.
Across the north-east, at least eight million homes and businesses are without power because of the storm, says the US Department of Energy.
Hospital blackout
Sandy brought a record storm surge of almost 14ft (4.2m) to central Manhattan, well above the previous record of 10ft during Hurricane Donna in 1960, the National Weather Service said.
Maryland appeared to have the worst of the rain and snow - with falls of 12.5in (32cm) and 28in respectively.
President Obama was due to tour disaster areas in New Jersey on Wednesday with New Jersey Governor Chris Christie.
Mr Christie, a Republican and supporter of Mr Romney's candidacy, went out of his way to praise the Democratic president for his handling of the storm.
"I spoke to the president three times yesterday," Mr 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."
Mr Romney resumed low-key campaigning on Tuesday, converting a rally into a storm relief event in the swing state of Ohio.
In all, storm Sandy has claimed well over 100 lives, after killing nearly 70 people as it hit the Caribbean.
Credit: BBC
