I think you will really enjoy Austin! I moved here about 4 years ago with 3 children, so I know how stressful that can be. Depending on your budget, there are some really nice areas right off of Capital of Texas Hwy that are in the highly sought after Eanes School District. Somethimes traffic can be pretty bad in that area, so looking in SW Austin might be another option, and you won't have as much of a traffic headache. That is the area I live in and I love it. You can get to downtown Austin within 15 minutes, but there are plenty of amenities nearby with good schools too.
Good luck with your move! If you would like any more information on the area or other suggestions, please let me know. I work in the largest real estate office in Austin with hundreds of talented agents, so I can find an answer to pretty much any question.
Thank you and have a great evening,
Keller Williams Realty