We have a few examples of stereotypes but we can't really build a "stereotype map" or anything. From Lucian he can find some passages like this (from Icaromenippus or The Sky-man):

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 wagons; half a turn in another direction gave me Egyptians at the plough, or Phoenicians chaffering, Cilician pirates, Spartan flagellants, Athenians at law.

And from the late Antique Gallic poet Ausonius we have this:

“This is Silvius Goodman [Silvius Bonus].’” “Who is Silvius?” “He is a Briton.” “Either this Silvius is no Briton, or he is Silvius’ Badman.’”

So apparently the British are bad at poetry. There are a few other examples like that which really enrich our understanding of the ancient world but are far from complete.