I wonder if the Rome of the Caesars had something like "the Greek District", "the Persian District", "little Alexandria" and so on.
/u/xenophontheathenian wrote an excellent writeup on ethnic quarters (or rather, the lack thereof) in rome
https://www.reddit.com/r/AskHistorians/comments/4zpkzv/how_did_the_different_ethnic_quarters_in_rome_and/