
The good news for you is that the Hyurs migrated to Eorzea centuries before your character would have even been born. There are likely more Hyur born in Eorzea than anywhere else at this point, so that's really not a concern.
But you mentioned playing a Highlander? They're a bit of a special case- many Highlanders are either refugees from or descended from refugees from the nation of Ala Mhigo, which was conquered by the Garlean empire about 15-20 years before the present day in the game. Not all of them are necessarily Ala Mhigan in ancestry, but the majority of that nation's population was Highlander prior to the invasion, and thus a large number of Highlanders trace their ancestry back to Ala Mhigo. When your character gets to a level in the mid-20s, you'll actually end up going to an Ala Mhigan community in the Thanalan region, and learn more about how they are living in the wake of losing their homeland, if you're at all interested in that backstory.
But if you don't want your character to be from there, there are Hyur in every major city-state, including the Elezen-dominated Ishgard. They've certainly been around for a long time, too, so don't worry about having to play a Hyur who has only recently migrated to Eorzea. You typically see the most Highlanders in and around Ul'dah, if that helps you at all to know.
But you mentioned playing a Highlander? They're a bit of a special case- many Highlanders are either refugees from or descended from refugees from the nation of Ala Mhigo, which was conquered by the Garlean empire about 15-20 years before the present day in the game. Not all of them are necessarily Ala Mhigan in ancestry, but the majority of that nation's population was Highlander prior to the invasion, and thus a large number of Highlanders trace their ancestry back to Ala Mhigo. When your character gets to a level in the mid-20s, you'll actually end up going to an Ala Mhigan community in the Thanalan region, and learn more about how they are living in the wake of losing their homeland, if you're at all interested in that backstory.
But if you don't want your character to be from there, there are Hyur in every major city-state, including the Elezen-dominated Ishgard. They've certainly been around for a long time, too, so don't worry about having to play a Hyur who has only recently migrated to Eorzea. You typically see the most Highlanders in and around Ul'dah, if that helps you at all to know.