I would also like to thank you for your service to our country...well done!
I had to post because, though I love Dinosaur Valley, it really is not the best place to go backpacking, especially if you want to be alone.
My vote is with
Big Bend National Park.
But then, I do like CyberCelt's suggestions also. I live in Cleburne and I would select Lake Whitney over DVSP out of those choices. In fact, I backpacked from my front door to Lake Whitney a couple of years ago.