The newly opened areas, including the French Quarter and Garden District, all escaped major flooding when the city was devastated by Hurricane Katrina a month ago before receiving a second blow from Hurricane Rita last week.
"This is my home. I will never leave New Orleans," said Virginia Darmstadter, 75, who has lived in the Garden District since 1984. Her husband is in a nursing home in Houston.
Their home doesn't have electricity and suffered water damage, which contributed to mold. The family planned to return to Houston this weekend after cleaning up a few things.
CBS News correspondent Sharyn Alfonsi reports that many returned to maggot-filled houses without electricity or water, so they came home only to find out that they can't stay. The water in New Orleans is still undrinkable, the hospitals are still closed and the EPA warns that even homes that don't appear heavily damaged could be filled with toxic mold, Alfonsi reports.
"As soon as we get electricity and my husband is strong enough to come back, believe me, I'll be back," Darmstadter said. "I've lived long enough to know that life is a wave, you move up and down. When you are down, you have to muster the wherewithal to face it."
Business owners have started tedious, sweaty job of cleaning up, mopping up and picking up, in the hope of reopening as soon as possible, reports CBS News Correspondent Jim Krasula (audio). Owners were allowed back into the city Thursday.
New Orleans Mayor Ray Nagin has pushed aggressively to reopen the city despite concerns raised by state and federal officials. Serious health hazards remain because of bacteria-laden floodwaters, a lack of drinkable water and a sewage system that still does not work, said Stephen Johnson, chief of the Environmental Protection Agency.
"There are a whole lot of factors that need to be weighing on the mayor's mind," Johnson said Thursday. He said the EPA was not taking a position on Nagin's plan. He declined to say whether he would allow his own family to return to New Orleans.
Alfonsi reports that the people returning to New Orleans Friday seemed to be safe, because it appeared that the police, federal officials, the army, and the National Guard outnumbered residents.
Along Prytania Street, people cleared brush and downed tree limbs from their yards as repair crews worked on power lines. Taylor Livingston, 40, was using a leaf-blower, hoping to create a lived-in look at three homes he is guarding against looters.
"I don't know how it's going to come together," he said. "I don't know if there's ever been a big city evacuated the way we were evacuated. It's all new. I don't know that we can come back that quick."
Business owners began showing up Thursday, some saying they were pulling out and others vowing to rebuild.
"We are lucky. I was expecting much worse than this," said Germame Kassa, whose Ethiopian grocery and deli was relatively unscathed, although the stink of rotting food wafted through the locked doors. "One way or the other, we'll be back in business."
State officials say at least 140,000 homes and businesses across southeastern Louisiana were so badly damaged that they must be torn down. The storms also left 22 million tons of debris, including 350,000 cars and trucks, said Mike McDaniel, chief of the Louisiana Department of Environmental Quality.
"Just as the nation knew that we had to create economic greatness in New York City after 9-11, the nation and the world needs south Louisiana," Louisiana Gov. Kathleen Blanco said in seeking federal tax breaks, incentives and grants.
Meanwhile, the Commerce Department said that people living in the areas along the Gulf Coast devastated by Katrina had suffered property losses totaling $100 billion that will not be covered by insurance. Because of this impact, personal incomes fell by 0.1 percent in August. Incomes would have risen by 0.2 percent had it not been for the hurricane.