Avoid at all costs
I'm afraid your concern is warranted as sadly that is exactly what it will be like. Texas in particular is flat, boring and huuuuuuuge. Many highways in Georgia have massive trees either side so you can literally drive for hours and see no landscape - it can actually get very claustrophobic. Not sure what time of year you're planning but the South in summer is hotter and more humid than most places on earth.
It sounds like you may have done some of the great American West but that would always be my first choice. This is what I would suggest
From the UK get a cheap flight to Vegas then drive 2 hours north to St. George (spectacular drive in itself.) From there you could go to Bryce Canyon, Zion National Park, Monument Valley, over the top of Utah to Moab or underneath to Grand Staircase Escalante. Moab is spectacular (one of my favorite places on earth) with Canyonlands and the extremely accessible Arches NP. Go slot canyon hiking in Grand Staircase and drive Utah State Road 12 - consistently duking it out with Pacific Coast Highway for the most scenic drive in the US. Go to Boulder Utah on Route 12 and see real cowboys bringing in their herds at sundown while you eat the best grass fed burger you will ever eat watching the sunset.
More off the beaten track is New Mexico which despite it's reputation has an extremely varied landscape and a fascinating history. In the south, White Sands park, a pin drop other planet feeling place. Then the solitude is shattered by fighter planes from the US Air force base next door conducting training exercises. Drive north stopping at family owned Mexican restaurants, visit the very large array, take the Breaking Bad tour of Albuquerque and onto Santa Fe one of the oldest trading towns in the US. Nestled in the mountains at 7500 feet above sea level it is beyond spectacular, and has the most number of art galleries per capita in the country. The north of the State has Los Alamos where the atomic bomb was developed and the foliage begins to gradually turn into Colorado as you get to the Hot springs area. Native American history and stories are everywhere in NM and learning about their culture and history is fascinating.
Anyways, that's my 2 cents but if you do make it Santa Fe let me know as I'll be there July & August