I would suggest that a "diner" is pretty close to what you are thinking of. It suggests a working-class eating establishment that is not part of a chain. Edward Hopper's Night Hawks is from 1942, but there are still establishments up and down North America that look pretty much like that except that the people inside are dressed differently.

(Also, greasy spoon is totally still in use as a term, although it means, basically, "diner where the floor doesn't get mopped as often as it ought.")