Caprock Canyons is a great park, and barely inside your 6 hour limit.
Fort Sill area, you have the old post and museum, as well as the Artillery Museum. Puts you in the area of Lake Atrus, Wichita Mountains wildlife refuge and Meers Store.
Caverns at Sonora, and Fort Concho are well within range
We do a lot of weekend getaways across Texas. Not really a hiker so our choices are more sedate. Here are my favorites:
Boerne -- stay at the Kendall. Great shopping and food on the Hill Country Mile. Breweries galore. All walkable. Lunch at Cibolo Creek Brewing; dinner at Peggy's on the Green or Richter Tavern. Get a massive cinnamon roll at Richter Bakhaus.
Brenham -- stay at the Ant Street Inn. Again, walkable downtown with shopping, wine bars, etc. Lunch at Pioneer Smokehouse or LJ's; dinner at Main Street Uncorked or 96 West.
Johnson City -- everyone knows Fredericksburg, but JC is an easier stay -- less crowded and less expensive, but still close to tons of wineries and only about 30-40 minutes from Fburg. Lunch at Vinovium; dinner at Bryan's on 290.
Galveston -- stay at the Tremont. Shop the Strand. Bars and restaurants galore.
Of course, there are the Hyatt and Hilton resorts in the Hill Country if you want something more upscale.
A lot of my Dallas friends head to Grapevine but I've never been. I'm sure folks here can fill in the gaps.
Waco makes a great long weekend. Mammoth National Monument, Dr. Pepper Museum, Texas Ranger Hall of Fame, Texas Sports Hall of Fame, Magnolia Silos, Caldwell Zoo, Waco Surf, Fort Parker SP, and lots of outdoor stuff on the Brazos and local lakes.