From El Paso, drive 100 miles east to Guadalupe Mountains National Park and stop at the Pine Springs campground and trailhead. Follow the 4.2 mile trail (one way) to the top of the peak.
Desert views are endless from the top of Texas. It can be very windy though. Late fall is a good time to go to see the incredible foliage display in McKittrick Canyon. The picture is taken from the summit, with El Capitan just below in the foreground.