To see a very different and very scenic part of Texas, take the Balmorhea exit from I10 and drive less than an hour south to the Davis Mountains. If you can, get a reservation at the Indian Lodge in Davis Mountains State Park, one of Texas' prettiest parks. Here's the link www.tpwd.state.tx.us/state-parks/indian-lodge
If the lodge is booked you'll find good choices in nearby Fort Davis. We like Hotel Limpia there. If your time permits, spend a couple of nights to allow a full day to enjoy one of our most scenic and interesting areas.
Things to do in the area include the McDonald Observatory, the 74 mile scenic loop through the mountains, and Fort Davis National Historic Site, the partially restored 19th century US Army fort which saw service during the Indian Wars.
I prefer the northern route across New Mexico and Arizona which to me is more scenic. If you do go through Carlsbad as Tet suggests, I would then head north to meet I40. Santa Fe is one of our most beautiful and interesting cities, only a short detour. Spend a couple of nights there if possible. The lodging and dining choices are superb.