If you're looking for a neighborhood that is close to downtown, accessible to all kinds of restaurants and nightlife, and still great for raising a family, then the central Austin area known as Brentwood, Allandale, Crestview is your spot.
You should live here if you love older homes, and prefer to live close to downtown. You may be just coming out of the partying stage as your family grows – you still want access to bars without actually going to any of them.
Crestview has the oldest homes, built in the 1940-50s, and are the smallest of this area. As with the Tarrytown area, and many other neighborhoods in Austin, because the homes were built quite small, they are perfect for teardown and rebuild.