The National September 11 Memorial Museum, built into the bedrock of the World Trade Center Twin Towers, documents the attacks, their impact and legacy with 10,000 artifacts.
It was inaugurated last week at a ceremony attended by President Barack Obama but on Wednesday ordinary Americans and foreign visitors got their first chance to visit.
Many of the first to emerge said they were reduced to tears by exhibits that include a crushed fire engine, powerful photographs and voice messages of those who were killed.
"I just cried. It makes you very sad when you see that up there in front of you," said Joseph McAuliffe, a 64-year-old senior probation officer from Jersey City.
Damaris Rodriguez, 61, who works for the New York state health department and whose daughter Amy is a 9/11 survivor, said she came to find peace.
"I thought it was amazing. It was very overwhelming," she told reporters, saying that the experience had brought the horror of that day rushing back.
Amy, who worked for Lehman Brothers, survived because she was late for work that day, coming out of the subway just as the first tower collapsed.
She was also survived the 1993 World Trade Center bombing and is now a teacher, too traumatized to visit herself.
"It was beautifully done. It was like pulling punches in the stomach," said Shannon Bailey, 43, an actor who was in New York on 9/11.
"It made me feel like I was going to a funeral."
But the museum has been no stranger to controversy. Its own religious advisors criticized its depiction of Al-Qaeda for being linked too closely to Islam.
Some 9/11 families have also been upset about a lack of dignity in transferring thousands of unidentified remains of victims to an underground repository at the site.
Amateur historian Todd Fine said the museum ignored the neighborhood's Arab American heritage in the early 20th century and failed to put Al-Qaeda into proper context.
By defining the terror network as "Islamist" and describing America's enemies in religious terms, it was fanning the risk of hate crime and stigmatizing Arab Americans, he said.
"When I saw that section about Islamism I became very scared," he told reporters, complaining that the museum should be federally run and leading historians consulted.
But many other visitors told AFP they avoided that section.
"I like that they didn't focus on that because that's not the point," said Gina Doost, a 26-year-old journalist who launched an online inspirational magazine.
She said she was most moved by posters of the missing and handwritten notes to loved ones.
"I didn't even want to look at that (Al-Qaeda part)," said Rodriguez. "It hurts me to think people could kill in the name of God. It's hard to see, why do they hate us so much."
Another bone of contention has been the gift shop, opposed by those who believe on principle that there should be no commercialization of what is a site of mass murder.
Among the items on sale is a $95 silk scarf depicting the Twin Towers and a platter in the shape of the United States, dotted with hearts in place of New York, Washington and Pennsylvania, where the hijacked planes struck.
"It would be like going to a cemetery and someone selling replica headstones or daisies just to make a profit," said Rain Dubilewski, a 24-year-old model from Vermont.
A few complained the $24 admission fee was a little steep, but others pointed out that it was in line with other museums in New York and that on Tuesday evenings it's free.
Museum president, billionaire former New York mayor Michael Bloomberg, has stressed the museum does not receive federal funding and will cost an estimated $60 million per year.