Head west to Big Bend Ranch State Park. Stop by the Barnock Warton Environment Education Center first to pick up your hiking permit for the park. Spend a few hours exploring the park; I recommend the Closed Canyon Trail and Hoodoos & Balanced Rocks Trail, which are along the paved road that runs through the park. If you have the time and the confidence in your vehicle, you can drive along miles of dirt roads to more remote trails; the park is vast and very lightly-visited. You can also raft along the Rio Grande.
Once you've explored Big Bend Ranch to your satisfaction, proceed to the border town of Presidio. You can visit Fort Leaton, a large 1830s adobe structure that has served as a trading post and fort. Continue on north to Marfa, a quirky, artsy town and home of the avant-garde Chinati Foundation. Eat in one of the many fine restaurants in Marfa and stay at the beautiful, classic Hotel Paisano. After dark, you may wish to head east of town to the Marfa lights viewing area to see if you can catch a glimpse of the mysterious phenomenon.
The next morning, head home. Enjoy your trip.