I lived in Dallas for four years and I can say with some authority that there is nothing within a reasonable radius of the city that can beat the Wichita Mountains
. Rugged granite mountains, wild bison, elk and longhorn and only a bit over three hours from the city. Add a dinner at the Meers Store and you can't beat it. You would have to go to the Transpecos or the Caprock to get anything near as good, but then you are looking at spending at least half a day in the car (if going to the Caprock, a full day to Big Bend).
The Hill Country is OK, but if you aren't looking for barbecue and music as well as some rocks, then skip it and head back up to the Wichitas.
Seriously, for that part of the world, they are tough to beat.