Like the run of a play itself, All About Eve takes place over a few months in the "present day" of time period 1950.
All About Eve couldn't take place anywhere else. Eve's scheme, which relies on her becoming Margo's understudy, wouldn't work in Hollywood or on television. Plus, theater actors look down on Hollywood, and everyone looked down on TV at the time. Addison even says, "That's all television is, my dear. Nothing but auditions." The sad fact was that in 1950, television was starting to seriously compete with movies for audience.
Despite taking place in the New York theater world, we don't see much of the city itself in this film. The action always takes place behind the scenes or in Margo's house or a restaurant, never on the streets of the city. There's one shot of Eve and Addison walking through the street, but they're in New Haven, Connecticut, and they are clearly walking in front of a backdrop, an embarrassing bit of film trickery that has not aged well.
The 1950s were a time when most women defined themselves by their relationship to a man. Even Margo Channing, a legendary actress, worries that she'll lose her man to a younger woman; when he finally proposes, she leaves her career behind. With strong female characters like Margo and Eve, you might think this was a feminist film. You'd be wrong.