The timeline of the Andal migration, the rise of Valyria and Valyria's displacement of the Rhoynish has always been unsatisfactory. However, IIRC Ran did say that the Valyrians and the Rhoynar did actually coexist for some time (hard to believe it'd be centuries, let alone thousands of years) before the Valyrians attacked them. So on that basis the Valyrian border would be the Rhoyne, with Volantis as their furthest outpost, with the rest of the Rhoynish kingdom to the north.
My personal preference would be for the Andal migration to either have nothing at all to do with the Valyrians, or if it to have been due to a religious vision which encouraged them to go to Westeros and leave no-one behind. But then again, that'd be the same reason why the Targaryens went to Westeros, which seems like implausible repetition.
I would use real world comparisons to try and find solutions to this vexing question.
If we look at tribes like the Goths that invaded the Roman Empire around the 4th century AD, these tribes were usually moving west and south into Roman territory due to the pressure of other aggressors further east.
In the same way, I would suggest that perhaps the Valyrian pressure in the East and South, forced the growing Rhoynish civilizitation to expand northwards and westwards into Andal territory. We know the Rhoynish were an older and more advanced civilization than the Andals - since the Andals apparently learned the art of ironworking from the Rhoynar.
So most likely the Rhoynar were too strong a foe for the relatively primitive and far less populous Andals to deal with. Hence, this pressure from the Rhoynar - as a knock on effect from the pressure of the Valyrians further east - forced the Andals to migrate to Westeros in turn, where they were able to defeat the even more primitive First Men, who were still in the Bronze Age at the time.
Most likely advanced technology spread from the east - either from Ashai or from Valyria - and crept westward first to the Rhoynar and then to the Andals and finally to the First Men, after the Andal migration, pretty much like it did in the real world, from the Middle East to the more barbarric European tribes in ancient times.
Thus, the Valyrians were ultimately still responsible for the Andal migration, but indirectly, rather than directly, through their encroachment into Rhoynish lands in the east.
Edited by Free Northman, 21 September 2012 - 03:59 AM.