The Chitauri are coming. Nothing will change that.
Grand Central Terminal
The majority of the battle of New York takes place on the Grand Central Terminal Viaduct above 42nd Street, just outside the Main Terminal. This is where Captain America, Hawkeye and Black Widow spend the majority of their time during the fight. The classic Avengers shot (where the camera rotates around the six heroes), takes place here.
Most of the action in this location was not shot in New York, but in Cleveland, OH or New Mexico. Reference imagery of New York was used to recreate a digital Park Ave into which the actors were placed.
Pershing Square
As the Chitauri stream from the portal, some civilians, including Beth the waitress, take shelter in the Pershing Square cafe, just outside of the Terminal.
MAP
(The Avengers, 2012)