re: Route Suggestions/Hotspots for Traveling America By Car

If you're bringing a tent, stop your first night at Colorado Bend State Park. Bring what you need. It's a 30 min drive or so over unpaved roads. It can be closed at times if the river is up significantly. There's a spring fed pool a short hike away. It's best after a rain when the water is cooler.
Further west would be the McDonald Observatory near Ft Davis. Beautiful country and night skies for sure.
I agree with the earlier mentioned Carlsbad Caverns as well. Do the full hike in and out. Don't take the elevator.
For nicer accommodations, stop in Ruidoso and play golf, ski, throw a few dollars on a horse race, or visit the casino. Nice little town. The All American Futurity is held over Labor Day. The Kentucky Derby of Quarter Horse racing. It's a busy town at that time, but plenty to do for sure.