The best answer I can give to this (slight caveat to come) is "probably". Regional stereotypes certainly existed, one of the better examples I like to give is from Lucian of Samosata (himself an Asian Greek who described being on the receiving end of prejudice) gave this short description of part of the world in "Icaromenippus", after the title character had flown to the moon and activated his power of an eagle's eye:

I could not go through the whole of it, even to please you; to take it in with the eyes kept one busy. But the main divisions were very much what Homer gives from the shield of Achilles: here junketings and marriages, there courts and councils, in another compartment a sacrifice, and hard by a mourning. If I glanced at Getica, I would see the Getae at war; at Scythia, there were the Scythians wandering about on their waggons; half a turn in another direction gave me Egyptians at the plough, or Phoenicians chaffering, Cilician pirates, Spartan flagellants, Athenians at law.

Explicitly, his vision does not just stretch spatially, but temporally, as these derive from a grab bag of stories from across classical literature. In this way it is quite representative of ancient ethnography from which stereotypes derive from, as general descriptions of places and people tended to reflect old tropes of classical literature rather than being "updated" to change with the times. Granted, there is a way in which this is typical of stereotypes generally--I remember the Futurama episode in which they go to an Atlanta that was more Gone with the Wind than Outkast--but describing haggling Phoenician merchants in the second century CE is a rather extreme example.

In his short book Tales of the Barbarians Greg Woolf argues that while there was a certain scientific quality to theorization of human diversity and ethnography in Rome, the actual "research" as such tended to be done in the library rather than the field. What this meant in practice is that descriptions of peoples and places tended to be quite anachronistic. With Pliny the Elder's descriptions of Gaul for example, you could be forgiven for thinking the place had not changed in the more than a century of Roman rule, and even in to late antiquity the image of the warlike, barbarian Gaul proved quite sticky. This is despite the fact that many of the people in Roman literary culture had first hand experience of imperial administration, and more to the point, many people from Gaul were important members of that scene (eg, Tacitus was from southern Gaul).

This goes down to what very few stereotypes we can get for individual cities, which tend to come from the classical period of the Greek city states. So Corinthian women would forever be flightily, Spartans would forever be brutish, Athenians would forever be giving speeches to the Assembly.

For the caveat I mentioned at the beginning: there is a reasonable amount of incidental errata and I certainly do not have comprehensive knowledge of it, so there may be an inscription in Pompeii that says "people in Stabiae smell bad" or something. But broadly speaking I am comfortable in saying that while direct evidence for direct city stereotypes is lacking, we do know of widespread stereotyping, and we do not there was some inter communal conflict (like a brawl between Pompeians and Nucerians at a gladiatorial match in 59 CE) so, to loop back to the beginning, there probably was!