You won't get more primitive, more solitude, more expansive Texas landscape and scenic vistas, more "WOW, this is why I love the outdoors" experiences than in
Big Bend National Park. If you're willing to make the drive, it will more than amply reward your patience and drive time. Plenty of folks here on WildTexas.com, including yours truly, have spent time in Big Bend. I haven't done backpacking out there, but we did camp in the Rio Grande Village Campground (in a rented pop-up tent trailer) in 2001. We intend to return for a tent camping/backpacking trip in the next year or two.