He'd seen photos, of course, but he wanted a firsthand look, so shortly after the former Iraqi translator arrived in this country, he made the trek with a friend, also an Iraqi.
"It was really an experience I'll never forget," he says. "Maybe some Americans don't recognize how important this symbol is for people who live under dictatorships."
It was the start of Albayati's remarkable journey. He moved from the squalor of Sadr City to the scenic beauty of Monterey, Calif. He went from unemployment to grueling labor at a chicken plant and construction sites to his current job as instructor at the Defense Language Institute Foreign Language Center, located on the California coast.
Albayati, 34, knows his is the typical immigrant success story in many ways: Hard work, determination _ and in his case, some helping hands.
Albayati also points out he regarded every experience in his adopted homeland _ even a brief stint at the chicken plant _ as part of a larger education that would lead to better things.
"It was a new place, a new culture, a new system, a new way of life," he says. "The way I looked at it was it's OK for me to struggle in the beginning. We are babies here. ..... I need to learn everything. You never learn without struggle."
Albayati made it to America with help from some members of the U.S. military, including Allen Vaught, now a Texas state lawmaker who was an Army reservist when the Iraqi was his translator.
Albayati helped Vaught understand the ins and outs of life in Sadr City, the tribal lineage, the religious makeup of the region and local customs and he identified the locations of schools and police and fire stations.
"He was a great friend," recalls Vaught, whose mission was to restore and rebuild Sadr City. "He really wanted his country to succeed. ... He helped me really understand how big the task was."
"You have to understand this is guy," Vaught adds, "that at any time I needed him to go on a mission with me, he did it. No questions. He said, 'OK, captain. Let's go.'"
When it became clear Albayati had made many enemies who wanted to kill him because of his translating job, Vaught and other members of the U.S. military worked to get their Iraqi friend here. They finally succeeded in 2007.
Albayati remembers pledging to the friend who picked him up in Chicago on his first night in America that he'd name his first-born son after him.
And he did. Daniel is now 14 months old. He also credits his success to Vaught, who opened his Dallas house to Albayati and his wife and helped them get their bearings.
"That first year, I couldn't have survived without Allen," he says.
Albayati still has family in Iraq and thinks often of the simple things he can do they can't because life remains difficult there. "It gives me some kind of sadness," he says. "My family says forget about it, don't think about it. Sometimes you can't help think about it."
Albayati, who travels in his work teaching Arabic and offering cultural training to members of the military, is a permanent U.S. resident. He hopes to get his citizenship in 2012 and is eager to vote.
"I don't really refer myself as an Iraqi," he says. "I say I'm from Iraq. ... Deep inside I don't really need a document to certify that I belong to this land. For me, sometimes I feel more American than some people born in America."