The previous moms have suggested great areas with excellent schools. Each part of town has its own vibe. If you have a really good Realtor they can help you find,, "your people", ha! The Arboretum area is very good. It is just north of what is now considered the "New Center of Austin", which is Northcross Mall on Anderson Lane and Burnet Road.
The Arboretum area feeds in to excellent public schools. Hill Elementary, Murchison Middle School and Anderson High School. All 3 of these schools have extremely active PTA's so you will be encouraged to be very involved. www.austinisd.org
You will be close to neighborhood parks. There are lots of churches, grocery stores, there is even a hospital over there.
Our daughter attended Stepping Stone Day Care. Many of them are Nationally recognized. The owner is very highly regarded all around the state and the Nation. Our daughter was completely prepared for kindergarten and they also offered information nights for parents. They offer all sorts of extras. Swimming lessons, evaluations, field trips, we loved it. We became very close to the other parents and children in her group.
My niece and nephew attended Elssas day care. They are part of the Crenshaw gymnastic Gym. They are also excellent.
Our daughter is now 19 so I cannot really recommend a pedi, but there are tons of great Doctors in Austin and of course we are so fortunate to have the state of the art Dell Children's hospital which is only about 15 minutes from that area of town.