Oki, I get it now. Ansburg no longer has a circle. But Vivienne is probably from Ansburg. Because Orsino was from Ansburg too.
Edited - Thought it was Tantervale because it's the 3rd largest city and was quite close to Orlais. Maybe she was from a rich family.. that's what get her into Orlesian politics in Montsimard....
Honestly, she could have been born in any Free Marcher city. However, she must have spent much of her life in a Circle.
The Free Marcher cities with Circles include Ansburg, Kirkwall, Markham, Ostwick, and Starkhaven.
I hope her background isn't linked to Hawke or the Inquisitor, so Kirkwall and Ostwick are out (in my mind).
People from Starkhaven seem to have vaguely Scottish accents, but Vivienne does not.
In my estimation, Ansburg or Markham are the most likely cities in which she was born and/or raised. Either Wycome or Hercinia on the coast of the Free Marches (and close to those two cities with Circles) could also be the city of Vivienne's birth, but not where she was raised necessarily. All four of those cities are also close to Rivain.
As far as her being from a rich family, it sounds too similar to the human Inquisitor's background. I think she might actually be from a poor family and has latched onto an upper-class lifestyle.
My speculation could be entirely wrong, though.