Yes, apart from Rome, Antioch and Alexandria which Pope St Gregory once referred to as the Petrine Sees, Constantinople, the New Rome, claimed it through St Andrew, Peter’s brother and then Kyiv in the northeast. Moscow took over that claim from Kyiv and called itself the “third Rome.”
Those were the major Sees founded by Peter directly or indirectly (not forgetting Jerusalem where at the Council of Jerusalem he clearly took a leadership role - even though the Church of Jerusalem could tell Peter what to do and “where to go” and he obeyed). In terms of smaller towns and villages throughout the East where St Peter established churches and consecrated their bishops, tradition indicates there were very many, in addition to the others the other Apostles established.
Rome was the only Apostolic, Petrine See in the West which situation lent itself to the Roman Pontiff’s eventual central role as the “chief administrative officer” of the Church. In addition, the constant infighting between the Ecumenical Patriarch of New Rome/Constantinople and the Byzantine Emperor led them to look to Rome, which by then was an insigificant Christian centre save for it being the See of the Successor of Peter, to act as a referee they could both accept. The Eastern Sees were a hotbed of theological and political activity where only an external (and removed) Pope could be trusted to make the call as to when fair play was to be had and when it was not. We have the records of a pope chastising, in writing, a Byzantine emperor even going so far as telling him he was a “boor” and “unmannered,” an assessment of an imperial personage that would earn anyone else the death sentence.
As in pagan Roman times, so too in the Christian era, appealing to Rome when the intrigues of Byzantium overwhelmed one was a welcome thing. The minutes of the Sixth Ecumenical Council, an entirely Eastern Council, show how the Eastern bishops and the Emperor tried to outdo one another in praising Rome and her popes (even Vatican I, which is accused of dogmatizing the zenith of papal jurisdictional power, did not go so far in praising the role of the pope). And whenever the Patriarch of Constantinople or the Emperor needed the Pope of Rome to especially be on their side, they strained every muscle to underscore the Pope as St Peter’s direct successor and therefore that should the Pope decide in their favour, he was to be obeyed by the opposing side without question.
But I digress . . .
Alex