While the film itself is set in New York, the Avengers Shawarma Shop is in fact based in Los Angeles. Elat Burger / Shalom Grill on W Pico Boulevard was the filming location for the memorable Avengers post credits scene, and I paid it a visit myself!
While there are obvious differences between the film and the actual shop in real life, it remains instantly recognisable due to the Snapple machine, and the curved counter. The tables are also identical, although the Avengers appear to have pushed two together, and even though the chairs look different, I believe only the edges have been repainted, so you may end up on a seat that was actually sat on by your favourite Avenger!
I believe the front of the counter may have had marble and tiling added, but the original wood and yellow version is still visible near the drinks machine.
Although most easily accessed by car, you can also visit by bus from Downtown LA.
You can read more about the scene here