From Las Cruces head east to Van Horn, TX. Take US 90 East to Marfa, TX. Plan on spending the night and view the Marfa Lights at the viewing center just east of town.
Continue on US 90 to Langtry, TX and the Judge Roy Bean Museum. You can dry camp there. Just ask the Host for the location.
Continue to San Antonio, TX. Visit the Alamo and do the River Walk.
Then head toward the Gulf by the way of Corpus Christi.
Visit Padre Island National Seashore. There is dry camping with a dump station & Water.
If you think you need more Gulf, head toward Rockport, TX. Several camping opportunities on the way.
Have Fun...