Moscow's Red Square may well be the most famous in the world, but never-to-be-outdone Manhattan boasts not one but two of its own.
The oldest is Little Red Square, located in Greenwich Village at Sixth Avenue and Bleeker Street. However, the site has nothing to do with Russia, but rather commemorates the Little Red Schoolhouse which sits adjacent to the square at 272 Sixth Avenue at Bleeker Street.
A bit odder is the Red Square, at 250 East Houston Street. The building itself has little to do with anything Russian, other than the roof, which features one of the last publicly-displayed statues of Vladimir Lenin to be found anywhere in the world. The statue is the work of sculptor Yuri Gerasimov, and was moved to the roof of the building in 1994 from its original location somewhere in the Soviet Union.
The statue was voted "Best Homage to a Foreign Despot" by the Village Voice in 2003.
(Top photo from http://en.wikipedia.org/wiki/Image:Lenin-east_village.jpg, below from http://www.forgotten-ny.com/STREET%20SCENES/deepsix/deepsix.html)