Isn't it interesting, though, that in all of the archeological revelations, there is never anything about the real daily life? Lots and lots of commentary about religious this and religious that, but never anything about ordinary daily life. Certainly, those fast food stalls would give us a picture of our ancenstors that we can understand. :)
Just off the top of my head, I can't think of any references to public restaurants in ancient Greece. Ancient Rome, yes, there were plenty of people living on the dole (some estimates as high as 400,000), and they often ate take-out food. Also, thanks to Pompeii etc, and especially the ruins of Ostia, Roman-era restaurants are well documented. Some were eat-in, many were just counters which could be opened to the street.
In ancient Greece, I suspect that "eating out" was dining at friends' homes.