What's more important for you, the destination, or the journey?
If the destination is the important goal (or if you are time-constrained), then hop on US83 in Shamrock, Texas, and ride the shoulder down to Leakey, Texas. 415 miles, straight shot, Route 66 to Southern Tier, done.
If the journey is the important goal (and if you have adequate time), here's a route from Elk City, Oklahoma to Bastrop, Texas filled with mountains (? yes!), lakes, a big waterfall, state parks, tiny towns and their fascinating and sometimes quirky museums, wineries, breweries, giraffes and dinosaurs. It's country lanes wherever possible (all paved). There are places to camp and motels at reasonable intervals.
I like riding through big cities -- IF I have a good route. Cities are the yin to the countryside's yang. Cities are where the biggest museums and best architecture are found. Cities are where you'll find large, well-stocked bike shops with good mechanics and camping supply stores. Cities have airports and train stations. Cities have Warm Showers.
This route crosses Dallas, something over half on bike paths and bike lanes and the rest on tree-lined neighborhood streets. If you just can't deal for whatever reason, that's cool: you can put your bike on Red Line light rail in Plano, switch to the #574 bike rack-equipped bus in Oak Cliff and pretty much skip riding the whole city - you'd miss the School Book Depository and the grassy knoll, though.
Give it a look. About 750 miles in five segments.
https://ridewithgps.com/routes/33140703https://ridewithgps.com/routes/33141010https://ridewithgps.com/routes/33146156https://ridewithgps.com/routes/33141072https://ridewithgps.com/routes/33150472
