Hello sc/out/s

I need some help. I live in New Orleans, and I have a break from work and classes coming up from March 21-30. I want to try and go somewhere mountainous, preferably within a 13 hour max driving range. Somewhere where backpacking and trailside camping is allowed too. Does anyone have any good suggestions?

I've been to Homochitto and a couple other smaller places, but I'd prefer something larger and with more wilderness.

Has anyone been to Big Bend National Park? Someone suggested that as an option.