We live in College Station and have done the drive several times with DD now 5 and DS now 3. Usually takes us about 16 hrs so depending on what part of Austin you live in, you probably can add about 1.5 hrs to that. I've done the drive alone and did it in just under 15 hrs. The time difference is based on the number of stops and their length. We stop every 2 hrs whether it's needed or not and try to group some of these with a gas fill-up while the kids hit the restrooms.
Depending on what time of the day we leave determines where we stop. If we leave in the afternoon, Baton Rouge or Slidell are good stopping points depending on how late it is. If we leave first thing in the morning, we go to at least Pensacola (several Marriott and Holiday Inn Express options) or try make it Madison, FL (Holiday Inn Express). I try not to drive to late into the evening as it takes the kids about an hour to settle back down and go to sleep after checking into the hotel plus it's just not worth getting that tired at the beginning of the vacation (WDW will do that for you).
Coming back, we normally leave between 1 and 2. Gives us a chance to do something in the parks and get a good lunch before strapping the kids in for the drive home. Normally both are sound asleep before we get off property. We normally then drive to the east side of Mobile Bay (6 to 7 hours). Lots of hotel options (Fairfield, Holiday Inn Express, etc.) before crossing over the bay.
Some stop options that I can remember are the Whaterburger in Orange, TX before crossing into LA. Chick-Fil-a in Slidell, La (fairly new and in a nice area), gas station in Madison, FL (newer and clean with several different options to get something to eay) and numerous McDonalds along the way.
We have a electric cooler that we put snacks (cheese sticks, drinks - water/caprisun, grapes, and summer sausage) in but still pick things up along the way for the kids to eat. The snacks cut down on the have to stops because they are 'starving'.
In addition to using our iPhones to find places along the way we picked up the book 'The Next Exit' at Cracker Barrel. It helps identify what options we have and how far until we can get there when we hear the dreaded words from the backseat.... 'I've got to go potty!'.
Enjoy the drive, it's worth it.
