I will confine my remarks to the route within Texas as I am very familiar with these highways. I will assume a starting point of Texarkana, Texas.
Look for the US 59 exit from I-30 indicated "Houston"
@ Marshall take Loop 390 around Northwest of Town to TX 43
@ Henderson take US 79 (loop around Palestine) all the way to
Rockdale then take US 77
US 77 will take you all the way to the vicinity of Corpus Christi.
Good commercial campground at Shady Pines, Texarkana (bit out of the way)
Good State Parks at Caddo Lake and at Tyler, require small modifications in the route above.
Slight modification allows visit to Bryan/College Station and the George W. Bush Presidential Library.
I could give many other alternate routes, but this is one for a start.