Maester Steven, I can't find anything on the borders of the Valyrian Freehold. They don't seem to have ever spread east of the Bone Mountains, but there's also nothing stating the Sarnorians or Qartheen were under their control. So, what are your thoughts on the extent of their territory?
The Valyrian empire did not extend into the lands of the Sarnori: “the confederation of cities later called the Kingdom of Sarnor survived the Valyrian expansion thanks to the great plain that separated one from the other.” Indeed, the Valyrians tended to look west rather than east (”once the Ghiscari wars had ended, the dragonlords of Valyria turned their gaze to the west…With the destruction of the Rhoynar, Valyria soon achieved complete domination of the western half of Essos, from the narrow sea to Slaver’s Bay, and from the Summer Sea to the Shivering Sea.”) for conquest.
The Lands of Ice and Fire are also helpful here:
Essaria (now known as Vaes Khadokh) was a Valyrian colony due east of Qohor, connected to the Free Cities by the Valyrian roads that connected the Freehold to its trading partners - to the port city of Saath in the north and Sarnath of the Tall Towers in the east. So we can conclude with a high degree of confidence that Valyria’s eastern border was somewhere around Essaria (perhaps at the banks of that enormous river?) and that at some point Valyria managed to work out a treaty allowing them to extend their roads into the Kingdom of Sarnor for the purposes of trade.
Further to the south, we can look to the extent of Ghiscari territory to guess at how far east Valyria extended once old Ghis was conquered. Krazaaj Has, Vaes Mejhah, Vaes Efe, were all Ghiscari colonies, but Yinishar and Adakhakileki were not. So I’d say the furthest east Valyria got through its conquest of Old Ghis is Vaes Efe.