"Nineteen firefighters lost their lives in the line of duty, and we as a nation stand together," she said through tears.
Liberty Island was decorated with star-spangled bunting, but portions remain blocked off with large construction equipment, and the main ferry dock was boarded up. Repairs to brick walkways and docks were ongoing. But much of the work has been completed since Sandy swamped the 12-acre island in New York Harbor.
The statue itself was unharmed during the storm, but the land took a beating. Railings broke, docks and paving stones were torn up and buildings were flooded. The storm destroyed electrical systems, sewage pumps and boilers. Hundreds of National Park Service workers from as far away as California and Alaska spent weeks cleaning mud and debris.
"It is one of the most enduring icons of America, and we pulled it off — it's open today," National Park Service Director Jonathan Jarvis said. "Welcome."
The statue was open for a single day last year — Oct. 28, the day before Sandy struck. It had been closed the previous year for security upgrades. Neighboring Ellis Island remains closed and there has been no reopening date set.
Nationwide, Philadelphia, Washington and New Orleans hosted large holiday concerts. A Civil War re-enactment commemorating the 150th anniversary of the Battle of Gettysburg drew as many as 40,000 people to Pennsylvania.
Also in New York, throngs of revelers packed Brooklyn's Coney Island to see competitive eating champ Joey Chestnut scarf down 69 hot dogs to break a world record and win the title for a seventh year at the 98th annual Nathan's Famous Fourth of July International Hot Dog Eating Contest. Sonya Thomas defended her title with nearly 37 dogs.
In his weekly radio address from Washington, President Barack Obama urged Americans to work to secure liberty and opportunity for their own children and future generations. The first family hosted U.S. servicemen and women at the White House for a barbeque.
Atlanta and Alaska held holiday runs — thousands raced up a 3,022-foot peak in Seward. In New Orleans, the Essence Festival celebrated black culture and music along the riverfront.
The celebratory mood turned somber in Oklahoma and Maine with fatal accidents during parades. In Edmond, Okla., a boy died after being run over by a float near the end of the town's LibertyFest parade. In Bangor, Maine, the driver of a tractor in the parade was killed after the vehicle was struck by an old fire truck.
Anti-surveillance protests cropped up in a number of cities on Independence Day, with activists speaking out against recent disclosures that the National Security Agency has been secretly logging people's phone calls and Internet activity. In Philadelphia, more than 100 people marched downtown to voice their displeasure, chanting, "NSA, go away!"
But in Union Beach, N.J., which was destroyed by Sandy, residents had something to celebrate. The working-class town won a party and fireworks contest from the television station Destination America and USA Weekend magazine.
"It's wonderful. Everyone's been so depressed," said Mary Chepulis as she watched a band perform on a stage that stood where the home next to hers had been.
Associated Press writers Bridget Murphy in Boston, Katie Zezima in Union Beach, N.J., Christopher Weber in Hermosa Beach, Calif., Stacey Plaisance in New Orleans and Colleen Long in New York City contributed to this report.