Genesis 11:2

And it was while they were journeying from the east that they found a plain in the land of Bavel, and dwelt there.

AS THEY JOURNEYED FROM THE EAST. Rashi comments: “They journeyed from where they were then dwelling, as it is written above, And their dwelling was from Mesha, as thou goest toward Sephar, unto the mountain of the east. From there they journeyed to search out for themselves a place that would accomodate them all, but they found none except Shinar.” But this is not correct for this is the account of the children of Shem only, concerning whom it was so said [that they dwelled at “the mountain of the east”], and why should Scripture attribute the dispersion to the descendants of Shem when the children of Japheth and of Ham were more numerous than they? Besides, their habitation in their countries was from Mesha to the mountain of the east, and the dispersion of the nations took place before they settled there, for the children of Japheth surely did not come from the isles of the sea, Verse 5. to the land of Shinar; rather, it was during the dispersion that G-d scattered them abroad upon the face of all the earth, and at that time they were settled in their lands, after their nations.
And Rabbi Abraham ibn Ezra explained that the mountains of Ararat are in the east. [Thus the verse before us which states, as they journeyed from the east, means as they journeyed from the mountains of Ararat.] That which he said is correct for the mountains of Ararat are in the east near Assyria, as it is said, And they escaped into the land of Ararat. And when Noah came down from the mountain [upon which the ark had rested], he and his sons settled in those lands, and when they increased they journeyed from there to this valley called Shinar.
According to our Rabbis, the men of the dispersion rebelled against their Creator. But those who pursue the plain meaning of Scripture say that their idea was only to be closely united, for Scripture declares their intention, lest we be scattered, and does not relate any other matter [motive] concerning them. But if it be as those commentators say, then the men of the dispersion were fools for how could one city and one tower suffice for all people of the world? Or perhaps they thought that they would not be fruitful and multiply, as it is written, and the seed of the wicked will be cut off.
However, he who knows the meaning of the word “name” — as they said, and we will make for us a name — will understand their intent and will know the extent of their evil intention in constructing the tower. And then he will understand the whole subject, namely, that theirs was an evil thought, and the punishment that came over them — to be dispersed in their languages and countries — was meted out measure for measure for “they mutilated the shoots” [of faith by seeking to undermine the principle of the Unity]. Thus their sin was comparable to that of their father Adam. Perhaps on account of this the Sages expounded: “And the Eternal came down to see… which the children of men had built. Said Rabbi Berachyah, ‘[Whose children could they have been but the children of men?] Perhaps the children of donkeys or camels? Rather it means the children of the first man, etc.’” Contemplate further that in the entire subject of the flood, Scripture mentions Elokim (G-d), while in the entire matter of the dispersion it mentions the Tetragrammaton; the flood came on account of the corruption of the land, and the dispersion came because “they mutilated the shoots” of faith and therefore their punishment was meted out by His Great Name. This explains the “coming down” and also the Divine measure meted out in Sodom. The student learned [in the mystic lore of the Cabala] will understand.

בנסעם מקדם, they were leading the lives of nomads, much like shepherds who move to wherever there was good grazing land for their flocks.

ויהי בנסעם מקדם, from the east, for this is where they had lived previously, and this was where G’d had created man before He placed him in Gan Eden. When Noach had come out of the ark he proceeded to the place where he had lived before the onset of the deluge. Also the mountain range of Arrarat is in an easterly direction (eastern Turkey and Georgia in southern Caucasus) Traveling eastward, the people had came to the valley of the Euphrates and Tigris which they found very much to their liking, a land which was called the land of Shinor. This land had already been mentioned in 10,10 as Nimrod’s first power base. We already explained that what is reported in that chapter actually referred to events after the Tower and the dispersal of mankind. Although the Torah did not elaborate on the meaning of the name Shinor, our sages in Shabbat 113 explain that the dead bodies (skeletons) of the people who had perished during the deluge had been swept down there by the rivers. It was the lowest place on earth far and wide.