Briar can adapt easily to new places, but she definitely prefers big cities. She likes busy places—such as Castelia, Lumiose and Wyndon, which are all cities she lived in at some point in her life— and cannot imagine a life in the countryside or something.

But if she had to choose a place, it'd probably be Wyndon, mostly because she's used to the place and knows it well. She also likes how modern the city is, and how it mixes both the businesses and entertainment in one place—in Unova things were different with both Castelia and Nimbasa.

A second option would be Hammerlocke. It's not as big as Wyndon but is also a place she could see herself living in. And being close to the Wild Area is a nice thing for her researches, too.

Other options could be Nimbasa City, Jubilife City or even Celadon City, just to mention a couple of ~new~ locations for her.