Using Atlanta's Transit System, MARTA
If you've done any traveling to any of the large cities of the world, you have probably used a subway or rail system to get around. These rapid transit systems are necessary and useful, and some cities are absolutely dependent on their subways.
In Atlanta, the system is called MARTA (Metropolitan Atlanta Rapid Transit Authority). As rail systems go, MARTA is an odd duck. It consists, essentially, of two rail lines that make a giant north-south/east-west X across the city and it's immediate suburbs.
It isn't large enough to be truly effective. It is also constantly hammered and derided in the local press. However, if by chance you use it regularly, you'll find the rail lines reliable and acceptable transport for families. MARTA also runs Atlanta's buses, and, well, they provide good enough bus rides. MARTA has regularly been prevented from expanding it's rail lines into something like an extensive and effective urban system (like New York's, Boston's, etc., etc., etc.) by local prejudices.
I can't guarantee you that a ride on MARTA will be a delightful pleasure, but I can say you'll probably be fine, and that most of MARTA's worst critics are alarmists with a political agenda. A bus ride is always a bus ride, of course, and you won't enjoy taking your family on MARTA's buses. If you have any need to go to Atlanta's Hartsfield Airport, use MARTA - it parks in the lobby! If you want to see the Atlanta Braves play, don't drive downtown - use the MARTA.
Any function in Midtown and Downtown is better reached by the MARTA system than by an expensive drive (parking fees are high and spaces are rare, if the price of gas doesn't worry you). This also goes for the satellite towns of Decatur and West End. Please be aware that some Atlanta attractions can require a hike of a half mile or more once you're off the trains. There are many other areas of interest in Atlanta that are a mile or more away from the rail lines (Fernbank Museum, Ansley, Buckhead, Vinings), and you will want to drive there rather than take the family on a bus. For the major locations I mention here, MARTA is the way to go!