Suggestions? Here go mine:

Tartessos - trading city in southwest Iberia
Knossos - on Crete
Sana'a - southern Arabia
Ur, Uruk, and/or Larsa - Sumerian cities to flesh out Mesopotamia
Massilia (unless Greek settler maps go there) - present-day Marseille, founded by Greeks
Sardis - western Asia Minor, capital of Lydia

I'm not sure if Tartessos and Sana'a fit on the map, but they'd be nice additions. I agree with the rest of your list except Massilia: it really should be founded by the Greeks (though it could appear later as independant if they don't colonize for some reason).

Petra: famous Nabatean city (but perhaps too close to Israel?)
Cirta: I thought we should try to represent Numidia but this is dangerously close to Carthage
Tigranakert: capital of the Armenian Kingdom (1st century BC)

Apparently Massilia was founded by Phocaea which was founded by Athens. So it could go on an Athenian settler map, but could be difficult.

Yeah, that might be a problem: the main Greek cities that colonized the Mediterranean are neither Athens nor Sparta; however we want the Greeks to colonize. Both civs should colonize according to their respective allies/subjugated cities (for instance, the Athenians should found Massilia, and the Spartans should found Syracuse). But both should have all the Greek colonies on their settler maps, only with a different priority order.

here are the cities in, so far:

Ur
Larsa
Susa
Troy
Taxila
Pattala
Tarsus
Aleppo
Knossos
Samarkand
Petra
Bactra
Gordion
Tushpa
Hasanlu
Sardis
Tayma
Amprakia
Gerrha
Sanaa
Artaxata
Sarmizegetusa

Yeah, that might be a problem: the main Greek cities that colonized the Mediterranean are neither Athens nor Sparta; however we want the Greeks to colonize. Both civs should colonize according to their respective allies/subjugated cities (for instance, the Athenians should found Massilia, and the Spartans should found Syracuse). But both should have all the Greek colonies on their settler maps, only with a different priority order.

yeah we need some historical research to be forwarded to city names, and eventually, settlers maps.
Both Athens and Sparta would have names of colonies founded by any other Greek city, but an higher settler value only for a direct colony or a colony of an ally.
For example, all Megara's colonies should belong to Sparta, if we follow this rule