Guadalupe Mountains National Park. The park's website says this about the trail:
"On a clear day, the view from the "Top of Texas" (8,749 feet, or 2,667 meters) is outstanding. The trail is very steep, but is well established. Some areas are exposed to cliff edges. It is rated strenuous, with 3,000 feet of elevation gain. The round trip distance is 8.4 miles, and generally takes 6-8 hours. Avoid the peak hike during high winds and thunderstorms."
For more regional hiking information, visit: www.texasmountaintrail.com/hike