Yes they did! Inevitably, given that the Ancient Greek world was divided into four major dialect groups, dozens of broad areas of settlement, hundreds of polities and federations, and over a thousand distinct political communities, there is more talk in the sources about what made Greeks different than what made them the same. A lot of this is politically charged 'othering' of the kind that leads to comical, admiring or dismissive stereotypes. For example:

• I wrote here about the Athenian perception of Spartans as uncultured, brutish hillbillies. They were known for their leisure-class affectations (including distinctly old-fashioned dress and hairstyles), their crude Dorian dialect and their economy of speech. The ancient tradition that the Archaic Spartan poet Tyrtaios was actually from Athens probably has its origin in the assumption that Sparta simply couldn't have produced such a talented poet. Thucydides famously said of the Spartan general Brasidas that he was a pretty good speaker - for a Spartan. The stereotype of terse Spartan (Lakonian) speech still exists in English, with the adjective 'laconic'. I wrote more about the perceived contrast between Athens and Sparta here. Non-Spartan observers also had a tendency to exoticise and objectify Spartan women, probably in large part due to their participation in religious dances and athletic exercise.

• I wrote here about how the Athenians saw the Thebans (and other Boiotians) as boorish peasants. Boiotia had few good harbours; its inhabitants were mostly known as landlubbers whose farms produced famously high-quality wheat. Even if Thebes was the setting of much of Greek mythology, its Classical inhabitants were therefore seen as farmers with little interest in the wider world. The stereotype wasn't helped by the fact that Hesiod, one of the great epic poets of Early Greece who wrote a poem about estate management, was a Boiotian. Later sources (especially Diodoros) constantly repeat the apparently unrelated stereotype that the Thebans were particularly physically strong and good at wrestling.

• I wrote here about the stereotype, ancient as well as modern, that Cretans and Rhodians were particularly effective as missile troops. Plato already argued that the small, warlike communities of the Cretan uplands were uniquely suited to the development of skirmishing warfare. Later on in Antiquity, the stereotype shifted, and Cretans came to be known as pathological liars and cheats.

• I don't seem to have covered this in detail, but another major stereotype was that the Ionians (the Greeks who inhabited many of the Aegean islands and the coast of Asia Minor) were cowardly and docile. Herodotos already connects this stereotype to the pseudo-scientific theory that the mild climate and fertile land of the west coast of Asia Minor naturally produces soft men accustomed to wealth and luxury. Its likely origin is in the fact that these Greeks spent much of recorded history under the control of different empires - from Lydian to Persian to Athenian to Spartan, then back to Persian, and so on. They resisted just as fiercely as other Greeks, but their position on the Asian mainland made it harder for them to do so successfully.

• Both the Ionians and their supposed ancestors, the Athenians, were considered excessively talkative. Reports of Ionians and Athenians representing their states at Sparta invariably revolve around the Spartans losing interest halfway through the speech, or simply not understanding what it is about. No doubt the origin of this stereotype lies in the greater role of the freedom to speak in the Assembly in these states. For Athenians, good oratory skills were a path to power and influence, whereas at Sparta this was not the case. The Athenians (and the Ionians) therefore spent a lot of time honing their ability to speak in public, and had a lot of patience for the oratory of politics; Spartans, not so much.

I'm sure there's a lot more that could be added. The English language contains at least one more Greek stereotype: 'sybarite,' from the famously wealthy and opulent Italian Greek city of Sybaris, which was effectively destroyed in 510 BC.