Depends on what you're looking for. Check out the map on Wikipedia: http://en.wikipedia.org/wiki/Neighborhoods_of_Atlanta
If you're looking for cute, fun areas, I like East Atlanta, Inman Park, Candler Park, Virginia Highlands, Druid Hills, Morningside, downtown Decatur and Emory. Ormewood, Grant Park, Reynoldstown, Edgewood, Cabbagetown, and Old Fourth Ward can be a touch dicey, but are in the process of gentrification, and very cute. I've never lived outside the perimeter, or west of 75/85, so someone else may be able to give you more info on those areas.