When we speak of theological schools in the early church, we do not mean anything like modern seminaries or Bible colleges. These were schools of thought. There was teaching going on, but more of a master-disciple relationship.
There were five patriarchal sees in the early church and these were Antioch, Alexandria, Constantinople, Jerusalem and Rome. Because of historical circumstances, the cities that had the earliest flourishing churches were Antioch and Alexandria.
These two cities were close enough in location (Egypt and Syria) that they had some interaction, but far enough apart that they had developed separately.
You can find out more about Antioch in the New Testament in this article and about Alexandria in this article.
The stereotype is that Alexandria was about allegorical interpretation of the Bible and the divinity of Jesus, while Antioch was about the literal interpretation of the Bible and the distinction between the divine and human in Jesus.
In truth, there was much more nuance than that, although that stereotype does have a kernel of truth. Alexandrians, from the Jewish Philo to the Christian Origen did emphasize an allegorical interpretation. However, even Origen did not reject literal interpretations.
If you want to learn more about what was going on in these two cities and how their theological schools differed, you might be interested in the blog post: Early Church Battle Royale: Alexandria vs. Antioch. I would also point you toward this article that attempts to downplay the differences in biblical interpretation within these two schools.
One of the things that is interesting is that as these two schools were debating the finer points of theology, they had no idea that within few short centuries, they would be taken over by the Muslim conquests.
