When doing your planning, be sure to differentiate between Padre Island and South Padre.
Padre Island National Seashore is near Corpus Christi. You can boondock on the beach there (in the national seashore or up by Port Aransas), although with a 40-foot motorhome you would have to be careful not to get stuck. Also, early October may be pushing it if you want to boondock--it might still be too sticky to sleep comfortably without air conditioning. There are RV parks in Port A, though, and Mustang Island SP and Padre Balli County Park across from Corpus have electricity, although both are just parking lots.
South Padre Island is across from Brownsville, on the southern tip of Texas. It's 400 miles from Austin, and 700 miles from Lubbock.