West Texas and south central are pretty different in many respects, but Innkeeper knows. He's an expatriate Texan.
He has some excellent suggestions.
I've lived in several small west Texas towns. My memory of the older towns is that there is always a main street down the middle and it is very wide. The streets were wide enough that you could park your car at the curb, and I don't mean paralell. The curbs were very high and some had little concrete steps up to the sidewalks. The sidewalks were almost like covered porches--think of the precursor of strip malls.
I was a child in the sixties, but I remember a Motts (five and dime) a drug store, a Piggly Wiggly. I'm sure there were many more, but those are the ones that mattered to me because they carried rock candy. West Texas towns were a lot like most small southwestern towns during that era. One thing to know about that regions--sixties or not--is that the weather is extremely harsh.
The wind in the panhandle is ferocious and causes frequent dirt storms. They actual cause "brown outs." The dirt storms turn things red and coat everything in red dust. I remember my aunt hanging out cloth baby diapers to dry after doing laundry. We had a big dirt storm. The diapers remained pink even after washing them with bleach. We had hail storms every spring. That region is also very prone to tornados, but it is flat as a pancake and you can see the storms coming for miles in advance. It is rarely a surprise.
Once I remember it raining in the middle of a brown out. The dirt in the air turned to mud and it brought traffic to a halt. It blocked out the sun. I was very scared.
Oh, and it's hot in the summer and freezing in the winter. Doesn't that sound like fun? On the bright side, the people are as nice and as genuine as you could ever want to meet.
I can't come up with titles and I stink at links, but I suggest searching Amazon or B&N for titles of memoires of people who grew up in that region. My mother is forever reading things like that.
Best of luck