From there, the authorities said, they had planned to travel about 100km north to an Air National Guard base at Stewart airport in their hometown of Newburgh to shoot down planes with a shoulder-fired Stinger missile.
The alleged plot failed because the FBI had been monitoring the men for nearly a year and an informant sold them dud weapons, making sure the explosives were inert and the missiles inactive.
Police said the suspects had criminal records and may have converted to a radical form of Islam while in prison.
They had no known links to al Qaeda, police said.
"It speaks to our concern about homegrown terrorism ... that in many ways is the most difficult to address"
New York City
The authorities said Cromitie was the leader of the group and chose synagogues after having said that "the best target was hit already", referring to the September 11, 2001 World Trade Centre attack.
"It speaks to our concern about homegrown terrorism ... that in many ways is the most difficult to address," Raymond Kelly, New York City's police commissioner, said.
"They stated that they wanted to commit jihad," Kelly told reporters, using a term that is sometimes taken to mean holy war.
"They were disturbed about what was happening in Afghanistan and Pakistan, that Muslims were being killed. They made the statement that if Jews were killed in this attack that would be all right."
Each man was charged with one count of conspiracy to use weapons of mass destruction within the United States, which carries a maximum penalty of life in prison, and one count of conspiracy to acquire and use anti-aircraft missiles, which also carries a maximum penalty of life in prison.
Marilyn Reader, a defence lawyer, told the court that Payen, her client who appeared in court separately from the other men and with an unexplained bandage on his head, suffered from schizophrenia and bipolar disorder.