NEW YORK (AP) _ Despite the freezing temperatures and the stifling security, Jessica Talavera knew she couldn't spend this New Year's Eve anyplace but in Times Square.
``We're here to celebrate the greatest holiday in the world in the greatest city in the world,'' said Talavera, 25, of Leonia, N.J., as she stood wrapped in an American flag. ``The terrorists tried to bring us down, but we're still standing strong.''
Her feelings echoed throughout Times Square, where an estimated 500,000 revelers stood Tuesday morning to greet the new year and the city's new mayor amid intense security in the wake of the Sept. 11 terrorist attacks.
``I think this says everything to the whole world,'' Michael Bloomberg said after reciting the oath of office to become the city's 108th mayor. ``No one's going to beat us. We are the greatest people and we care about each other, and we are here tonight to celebrate together.''
Both the goodbye to 2001 and the hello to Bloomberg and the new year came off without a hitch. Bloomberg was sworn in by outgoing Mayor Rudolph Giuliani shortly after the Waterford crystal ball dropped from One Times Square to signal the arrival of the new year.
Many in the crowd said they had responded to Giuliani's post-Sept. 11 call to help New York get back on its feet.
``I think it's especially important to celebrate here this year because of all that has happened,'' said Mellonie Meitin, 30, of Miami, who was in Times Square on her first trip to New York.
``Even though we're from Miami and we didn't lose anyone Sept. 11, we feel for the people who did,'' she said.
Red, white and blue were the dominant colors at the 97th annual event. Many people waved small American flags; one small child was decked out in a red, white and blue snowsuit, a nod to both patriotism and temperatures that dipped into the mid-20s.
Smaller celebrations were held across the country, from fireworks in Las Vegas, Philadelphia and Seattle to a bash at an Anchorage, Alaska, bar featuring a Canadian rock band that plays ``The Star-Spangled Banner.''
Some celebrations _ including Denver's citywide party and fireworks in New York's Central Park _ were canceled. About 20 U.S. communities also dropped their First Night events because of terrorism fears or lack of money and volunteers.
In Boston, city officials estimated more than 1 million people took part in the city's 26th annual First Night celebration _ the oldest in the country.
In Hartford, Conn., revelers at the city's New Year's Eve celebration at City Hall were given the opportunity to reflect on the events of 2001 by writing any regrets on a scrap of paper. The scraps were to be tossed into a bonfire.
Cheap hotel rooms and a half-million dollars worth of fireworks helped lure revelers to Las Vegas' glittery Strip. The Las Vegas Convention and Visitors Authority predicted 282,000 people would come to town to mark the new year.
The New Year's celebration in Times Square was New York's largest event since the Sept. 11 attack at the World Trade Center killed nearly 3,000 people.
A few miles to the south, dozens of rescue workers continued digging Monday night through the trade center ruins.
``I'm just looking forward to a new year,'' said firefighter Larry Muccini, one of dozens of firefighters and police officers taking part in the round-the-clock effort in lower Manhattan.
In Times Square, security was as tight as for the millennial celebration two years ago, with about 7,000 police officers on duty. Despite the immense crowd, police reported just two arrests: one for public urination and another for disorderly conduct. A summons was issued for marijuana possession.
Several of the officers carried a new anti-terrorist weapon: radiation detectors, which could turn up any radioactive bombs. All wore black bands across their badges, some with the words ''9-11 NYPD,'' in memory of the Sept. 11 victims.
There were other nods to the terrorist attacks.
Logan Miller, 7, rang a bell onstage at Times Square in a special ceremony to honor the victims of Sept. 11. Bells were simultaneously rung at churches citywide.
Miller, whose uncle Mitch Wallace was a state court officer killed during the World Trade Center rescue effort, handled his duties as Times Square fell silent.
The crystal ball itself was engraved with the names of several New York firefighters, police officers, Port Authority and medical workers killed in the rescue effort. The names of every country and state that lost people when the hijacked planes hit the twin towers were also engraved on the ball.