I only checked a few before determining that all were easy to find if you looked at the report. With that said I think your list is close to correct but there is more than one incorrect.
You have to use the supplemental appendix from the paper [0] to figure it out. There are 23 samples, some of which come from the different treatment plants in the same city so that there are 10 cities represented.
[0] https://www.nejm.org/doi/full/10.1056/NEJMc2405937
The West Texas city (4 samples) is undoubtedly El Paso.
One of the North Texas cities is Wichita Falls.
I believe the other North Texas city is Lubbock.
There are four East Texas cities.
There is one Central Texas city. Three samples were taken and based on reported population served at the sample sites the city will either be Austin or San Antonio.
There are two South Texas cities.
So my list is
Wichita Falls - North Texas
Lubbock - North Texas
Both have excellent exposure to agricultural operations and lie along migratory bird flight paths.
El Paso - West Texas
This is the only city in West Texas large enough to have a wastewater treatment operation to serve the reported population numbers and it is also in an area with excellent exposure to agricultural operations.
Austin/San Antonio - Central Texas
This is a toss-up between these two since it could be either based on the population size reported for the wastewater treatment site and it is probably Austin based on designation as Central Texas city.
If San Antonio is considered a South Texas city then it will be one of the two South Texas sample locations. It makes sense for San Antonio and Austin to both be tested so it is likely that this paper places San Antonio in South Texas. I always considered it Central Texas (where I grew up) since it was just a short ride down I-35 and Laredo felt a lot more like South Texas. I'm probably wrong and it is indeed a South Texas city.
It's hard to guess the East Texas cities without digging into demographics and GIS data.
I suspect that Houston counts as East Texas though I always break things down differently since I lived there for a while. I consider it to be Rectal Texas. Just kidding, maybe.
It is likely that one of the East Texas cities sampled is Tyler since it is smack-dab in the middle of poultry country. Houston, classed as an East Texas city would be another. The other two could be suburbs of Houston or smaller towns in deep East Texas where there are a lot of cattle and chickens raised.