"We have to remember. It's a way to honor them," she said.
Members of the public included Nancy DiGiacomo, who came from Huntington, N.Y., with her husband, 9-year-old son, mother and sister.
"I just thought it was important to see" the transformation of the tragedy's wreckage, said DiGiacomo. "From that, something else can come of it."
Lt. Cmdr. Colette Murphy, a Navy spokeswoman, said she was excited for those serving on board to see the city's "awe-inspiring" welcome.
At a short ceremony later at Pier 88 near the site of the aircraft carrier, the USS Intrepid, Mayor Michael Bloomberg said the USS New York couldn't have a more fitting name, representing freedom, courage and resilience.
"This ship is actually a physical representation of that spirit with steel from the World Trade Center built into its bow so every friend that sets foot on it and every foe that dares challenge it will feel its power and know that it is literally made from the heart and soul of the city that has scarified so much," the mayor said.
Of the 361 sailors serving aboard the ship, around 13 percent are from New York state, which is higher than would normally be the case, Murphy said. There were many requests from Navy personnel to serve on the ship, which will carry some 250 Marines.
After the ground zero stop, the ship -- escorted by about two dozen tugboats and other vessels -- headed up the Hudson River toward the George Washington Bridge. After a U-turn there, it headed south to Pier 88. An official commissioning ceremony is scheduled for Saturday.
The New York will remain in the city through Veteran's Day and then head to Norfolk, Va., for about a year of crew training and exercises, Murphy said.
The ship is 684 feet long and can carry as many as 800 Marines. Its flight deck that can handle helicopters and the MV-22 Osprey tilt-rotor aircraft.
It was scheduled to be built before the terrorist attacks. About a year later, the announcement came that the ship would bear the name New York to honor the city, state, and those who died.
It's the latest in a line of Navy ships to bear that name. The others included a Spanish-American War-era cruiser, a battleship that served in World Wars I and II and a nuclear submarine retired from the fleet in 1997.
The ship is technically known as a San Antonio-class amphibious dock vessel. Four vessels in that class are in service, the USS San Antonio, USS New Orleans, USS Mesa Verde and USS Green Bay. Four others are being built. Of those, two also have been named in connection with the Sept. 11 attacks.
The USS Arlington was named to honor the attack on the Pentagon. The USS Somerset was named after the county in Pennsylvania where United Airlines flight 93 crashed.