If you take I-37 it's roughly two and a half hours.
There is about 130 miles between San Antonio, Texas and Corpus Christi, Texas. Although it is possible to drive a flight may be faster and should only take about 45 minutes.
3 hours
16 hours
144 mi - about 2 hours 11 mins
It is 1,403.21 miles according to MapQuest.
It is 1,128.33 miles accordng to MapQuest.
4 hours
The shortest time is 2 hours and 30 minutes.
Mapquest says it would take you about 26.5 hours to drive the 1697 miles between the two cities.
According to Mapquest, 1480 miles with a drive time of 22 hours, 36 minutes.
San Antonio, Austin, Dallas, New Orleans, Little rock, OKC, Corpus Christi, S. Padre, Mobile, Jackson M.S., Pensicola, Lake Charles, Baton Rouge, Memphis.
Google Maps estimates the driving time as 19 hours and 39 minutes.