Certainly. Granted, we only hear snatches of things like this, but there is one nice passage in Lucian (Icaromenippus, 16) in which the narrator lists things he saw when he was flying around:

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 haggling, Isaurians thieving, Spartan flagellants, Athenians at law.

The activities engaged in are clearly stereotypical for the regions: Isaurians are thought of as bandits, Athenians are litigious, Phoenicians are hard nosed merchants, and so on. We can't construct a stereotypical map of the empire or anything, but we have some hints.