If you plan to drive around/across Texas, I recommend you stay off the Interstate highways. They are crowded with lots of traffic (except in west Texas), lots of construction is happening (and will continue, it seems, forever), and you can make excellent time (if you are in a hurry) on the US and State routes.
What many non-Texas don’t realize is that the State Highways are usually excellent and fast and in good condition. It is common to see a posted speed limit on a Texas (not US) highway of 75 mph! While on the subject of speed, for example, the Texas State Highway 130 (SH 130), also known as the “Pickle Parkway,” is a Toll Road from near San Antonio, going roughly north, to near Georgetown (this route bypasses Austin’s traffic nightmare). This highway is noted for having a speed limit of at least 80 mph (130 km/h) along its tolled section. The 41-mile (66 km) section of the toll road between Mustang Ridge and Seguin has a posted speed limit of 85 mph (135 km/h), the highest posted speed limit in the United States.
Another good non-Interstate route east and west is US 380. We have driven this across Texas when we head west from the Dallas (or North Texas) area. Yes, you pass through a few towns but the traffic is light, the highway has been good, and the speed limit on portions of this was 75 mph. In west Texas, when you get to the town of Brownfield (on US 380), use their city campground. They have electric and water and a dump station—all free! Stay on US 380 and you will eventually go through Roswell, NM (not all that exciting) and end up near White Sands National Monument (definitely a worthwhile stop).
Driving in Texas often results in some pleasant surprises. For example, it is common in southeast Texas for a two-lane highway to have a wide “shoulder”—one that is wide enough for a semi to pull over and be completely out of the driving lane. What will happen (and this is very common) is that if you come up behind another vehicle going slower than you, they will most likely pull over onto that shoulder so you can pass and stay in your driving lane. You will appreciate the gesture.
Another surprise is that many Texas towns will have some tiny, but very interesting, local museum. Take advantage of these. They are often extremely cheap, maybe free, or they just ask for a donation. A visit is nearly always worth the time. I thoroughly enjoyed visiting where Judge Roy Bean held court in Pecos, TX.
The history of some of the towns you will pass through is sometimes a surprise. Recently, on our way to Bryan/College Station (home of Texas A&M), we passed through “Old Dime Box, Texas.” I don’t care who you are, a name that bizarre will get your attention. Why in the world would they name a town with that? Some quick research showed that one story was… When the first settlers here wanted to send a letter to someone, they would leave their letter and a dime in the box. Whoever was going to the nearest town (Caldwell, Texas) to get supplies or whatever would just take everyone’s letters and the dimes (to pay for postage) and mail everything. If anybody had letters coming back, they would bring the letters back to the box. It was an honor system and it worked.
Also note… There is a “Dime Box, Texas,” too. In 1913, the railroad moved and built a new line three miles from the original site of Dime Box. Nearly all the settlers moved to the new railroad location. So the original “Dime Box” became “Old Dime Box.”