The four, all Muslims, are to appear in a federal court later.
They were named as James Cromitie (also known as Abdul Rahman), David Williams (aka Daoud and DL), Onta Williams (aka Hamza) and Laguerre Payen (aka Amin and Almondo).
A senior FBI official in New York said three were US citizens and one was from Haiti.
BBC defence and security correspondent Rob Watson says the case appears to be a classic sting operation against suspected home-grown militants rather than a plot with any links to known international terrorism.
New York Mayor Michael Bloomberg said the alleged plot showed "homeland security threats against New York City [were] sadly all too real".
The arrests were the result of a year-long investigation, officials said.
The Riverdale Temple was one of the targets, the authorities say
"The defendants wanted to engage in terrorist attacks," said Lev Dassin, acting US attorney for the Southern District of New York.
"They selected targets and sought the weapons necessary to carry out their plans."
According to prosecutors, the men planned to detonate cars packed with C-4 plastic explosives outside the Riverdale Temple and the Riverdale Jewish Center in the Bronx district of the city.
They also intended to target military planes at the New York Air National Guard base at Stewart Airport, 60 miles (85 km) north of New York City.
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