Where does the manga Otoyomegatari take place? I know it's located near the Middle East, but I'd like a more precise idea of the locations involved in Otoyomegatari.
If you are not already aware, the series is set in 19th century Central Asia. The culture is without a doubt Turkic.

The main setting of the story is explicitly mentioned to be a rural village near the Caspian Sea. 



It's important to note that the land and territory borders in the 19th century were vastly different from what is is today. 



This bit, done by the author for the 2014 Taisho Award, sheds some light on the regions each of the characters are from.

Karluk's town (Pariya included) is located in modern Uzbekistan, and are of Uyghur ethnicity.

The city where Mr. Smith meets Talas, Karaza is likely in Karakalpakstan, part of Uzbekistan.

The town where Mr. Smith and his guide meets the twins (Laila and Leyli, they're Tajik. Not Turkic, but rather Persian) is Muynak/Moynaq, a city in northern Karakalpakstan.

Amir and her family are of Kazakh ethnicity, and hail from modern day Kazakhstan.