Texas allows overnight parking at any rest area operated by TXDOT. There may be one or two with a 'no overnight parking' sign but I have not seen them. I posted a map of the Rest Areas below. We have never had a problem parking overnight at any Texas Rest Area. They are generally well lit and relatively safe, and Texas has spent millions in the last several years "updating" them. We often stop at the one near Seguin on I-10 on our way to Houston, because it is staffed by volunteers who usually have some freebies like a cold drink, a sandwich, a cup of coffee and some friendly conversation. We even had a spaghetti dinner at one of the rest stops free of charge. There are still a few that have not been renovated or expanded, but those are generally the I-10 corridor and I-20 corridor west of I-35. One tip: If you are towing a trailer it's best to use the "trucks" side of the rest area rather than "cars" side. The spaces are pull through and it's easy in, easy out.
"You can't buy happiness, but you can buy an RV. And that is pretty close."