L.A.
Get on I35 heading South.
Stop in Austin to see the Capitol, The LBJ Library, Visit Zilker Park ride the little train, and swim in Barton Springs and eat at least one meal from a food truck.. There are also lots of free family things going on in Austin, so check online.
Along the way.. Stop in New Braunsfels and go to Schlitterbahn the original Water Park of Texas. Eat a German meal .Maybe try to get by Gruene Hall, one of the oldest Dance Halls in Texas..
San Antonio is lots of fun. It is so different from any where else in Texas.. The historical Alamo, The the fun of Sea World. Fiesta Texas, ok I know it is Six Flags, but it is a bit different. And make sure you spend a couple of days at the La Contera Resort. I have only heard wonderful reviews. http://www.resortlacantera.com/