Heres one:

In Pliny and Trajan's Correspondence, Pliny writes about a huge Gymnasium which has been erected overbudget and over deadline, on soft ground, badly. He asks whether Trajan thinks it should be abandioned, pulled down, or finished.

Trajan, amongst other things, says "Those silly little Greeks cannot keep away from Gyms."

I don't suppose that can truly be a stereotype, but the idea that an Emperor and a [Governor?] could be this candid about it suggests a certain degree of common parlance

ninja-Edit

http://www.wavcott.org.uk/revisionsite/classics/plinybyth.html <- Abridged bullet-pointed items in Pliny correspondence for short-referencing. Bonus: The quote I included is spelled wrong in this link

I found a good Source which requires you to be a member of academia.edu to download. A little taster of what he says were stereotypes of Egyptians, Jews and Phoenicians:

• "Greek and Roman Stereotypes of the Jews are reminiscent of, and mostly less extreme than, their views of other oriental nations [wise, mystical, exotic]...positive references to the Jews' antiquity, religious beliefs and customs, social customs, and moral rectitude... No mention of Jews in Roman records of scholars travelling to the orient to study science or academy (unlike numerous accounts of people gaining great learning from having travelled to Egypt, Babylon, Persia etc). "The Jews were the only people to successfully resist Christianisation, and only then do they gain their 'odd men out' in Western History", relative to the region.
• Egypt: "Supreme antiquity... fabulous monuments... stupendous riches... sublime religions. "Character flaws of cowardice, servility, rebelliousness, haughtiness... played second-fiddle to bizarre religious practices"... "the most superstitious of all people". "Egyptians attempted to claim any aspect of Greek culture as their own"
• Phoenicians: "character flaws... piracy, greed, cruelty, faithlessness, deceitfulness... in every possible literary context". [Herodotus]: "Phoenicians abandon [unseemly] circumcision when they travel to Greek areas"... "a nation of travelling salesmen, always willing to adopt alien ways of life"