The Dornish have certainly had maesters for some time, at least as long as the Targaryen conquest, so I doubt they’d have none.
The Iron Islands is tricky. WOIAF doesn’t say that Quellon was the first Ironborn to bring in maesters necessarily, just that he brought in dozens of them. My guess is that Harmund the Host probably was the first Ironborn to bring in maesters, but that they didn’t stick around due to the Shrike’s rebellion and the war of the Famine Winter. (Similar to how Balon banished maesters from his court.)
The North has had maesters for at least 500 years, based on the maesters’ records at White Harbor. It’s probably been longer than that, because there were maesters at the Wall since the Feast of Skane. If I had to guess, I’d say that maesters have been in the North at least since the Manderlys came from the Reach, so at least the last 1000 years.
Beyond regions, I think it comes down to the bottom reaches of the nobility, the least lords, poor landed knights, and the like, who couldn’t afford the fees.