If you are like me and don't drive over 65 mph while towing, a US highway works as well as an interstate. So, if I were doing your trip, I would take US 281 all the way to I-90 in South Dakota.
We have traveled nearly all of that route and it is good road with 60-65 mph speed limits. You will not have any major cities, difficult terrain, or toll roads to traverse. That route avoids not only the D-FW area, but the OKC, Wichita, and KC-Lincoln-Omaha areas. The biggest cities you will go through are Wichita Falls, TX, Lawton, OK, Grand Island, NE, and Sioux Falls, SD.
Most of the route is in the greener, tall-grass prairie portion of the Great Plains, not the really dry, brown part. A couple of not-to-miss places along US 281 are the Willa Cather House and Museum in Red Cloud, NE, and the Corn Palace in Mitchell, SD. I also enjoyed the Stuhr Museum in Grand Island and the Hastings Museum, but I am interested in history, trains and cars, and fossils, so they may not be of interest to everyone.
Have fun, no matter which route you take!
