Robstown is a city in Nueces County, Texas, United States, and a western suburb of Corpus Christi. It was founded circa 1906, and was named …Robstown is a city in Nueces County, Texas, United States, and a western suburb of Corpus Christi. It was founded circa 1906, and was named for Robert Driscoll. The population was 10,143 as of the 2020 census.