Alice,

I would not suggest anything near that ZIP code.  It's not a safe area.  Depending on your budget and living preference, Atlantic Station or other areas in Midtown might work for you.  They're not too far, but I would not recommend the area if you have kids. They're not the safest in Atlanta.

Collier Rd (just North on 75) has a number of nice apartments that are safer.  Post Collier Hills, for example.

Further to the North is a neighborhood (city) of Smyrna.  A number of apartments can be found there at any price range.  Several people from this forum live there.