I don't believe anyone rents modified Jeeps, at least not in the area. In any case, the wheeling scene is only serious in a couple of places here, and a standard rental JK will get you into as much trouble as you'll need. I suggest looking for companies that rent JKs, buying the insurance, and playing on some lighter trails in that.
If you visit Dallas, you have to go to the Fort Worth stockyard, visit Arlington to see the stadium and Six Flags, spend some time in Dallas proper (It's a few days in and of itself), and depending on what you like, there are all sorts of things to do in the metroplex.
If you go to Houston, I don't know as much, but you might try to drive to Galveston to the beaches, or to Austin and slightly north for a taste of what German settlers did in Texas. (Mostly, sausage and some city names. New Braunfels, most famously) I wouldn't really call Houston itself a tourist destination. Their stadium isn't as cool as ours, and the city smells like oil.
Either way, you MUST eat at Whataburger. It's a fast-food burger location founded in Texas, and the burgers are great. My personal favorite is the Double-Meat whataburger with cheese, plain and dry. I always tell tourists to eat Whataburger at least once on the trip. (Fun fact: Houston is so obese, there are 56 Whataburger locations within the city)
1997 Grand Cherokee Orvis Edition
Because tacky green leather is SUPER COOL