The distance between downtown Austin to downtown Laredo is 236 miles which if you drive it will take 3 hours 37 minutes if there isn't a lot of traffic in I-35 especially in San Antonio.
149 miles taking this route: Take U.S. 183 NORTH (and SH-183 TOLL - NORTH) out of Austin to U.S. 281 NORTH in Lampasas [63 miles]. Continue on U.S. 281 NORTH to Stephenville [86 miles].