Candler Park and Lake Claire are perfect for you. Both are assigned to Mary Lin Elementary School which is one of the best (if not the best) elementary school in the Atlanta Public School District and is often ranked in the top 25 elementary schools in Georgia. Despite having easily accessible top private schools nearby, over 95% of elementary-school-aged children in its assigned territory attend Lin.
As far as going out, there's a MARTA train station in the Candler Park neighborhood which means most of Atlanta's entertainment districts or stadiums are easily accessed. Most of our date nights are either by train or Uber/Lyft.
As far as quiet, the more East you go, the quieter. Little Five Points is on the Western edge of Candler Park and is a major tourist area. So if you live within the few blocks are to the west, you get the benefit of having great restaurants a short walk away, but it's busier. Further East (and especially in Lake Claire) you are away from the bustle.
Good luck!
