Eorzea's a pretty diverse continent, so you can have your character be born anywhere. While some races and clans are more likely to be found in certain places, they don't have distinct nations like they do in, for example, World of Warcraft.
With that said, it seems Keepers of the Moon are more numerous in the Black Shroud/Gridania and maybe La Noscea/Limsa Lominsa. Still, seeing how the city states are friendly to each other, it shouldn't be hard to come with reasons why your Keeper was born in Ul'dah or Thanalan.
I don't see why a Miqo'te couldn't want to be an arcanist. The arcanist guild-master is a Miqo'te (I think Sun-Seeker, but he appears exactly once), and the "second in command" is a Roegadyn. There's no lore forbidding races from being certain classes. So go wild with that!
With that said, it seems Keepers of the Moon are more numerous in the Black Shroud/Gridania and maybe La Noscea/Limsa Lominsa. Still, seeing how the city states are friendly to each other, it shouldn't be hard to come with reasons why your Keeper was born in Ul'dah or Thanalan.
I don't see why a Miqo'te couldn't want to be an arcanist. The arcanist guild-master is a Miqo'te (I think Sun-Seeker, but he appears exactly once), and the "second in command" is a Roegadyn. There's no lore forbidding races from being certain classes. So go wild with that!