Peachtree City is a swift way to meet all of your goals.
Regardless, you have a few good options with good school districts in Douglas, Cobb, Southwest Fulton and Fayette counties. That being said, Intown Atlanta has many safe communities with good schools near a golf course that also offer easy airport commutes. In my opinion, we have cooler things to do like live music every night, world class restaurants, and gorgeous parks and tree lined neighborhoods with a little bit of history.
Depending on how you like to commute, you can expand your horizons Eastward into Decatur and Northward toward Sandy Springs and use the MARTA rail system to the airport.
Depending on your price point, I suggest Grant Park or Ormewood Park, which are in very good elementary Charter school districts. The East Lake CC and Charlie Yates course are only 9-10 minutes East.
Of course, Intown Atlanta's Candler Park has a fun 9 hole course and some terrific houses within walking distance of the expansive Candler Park.
One of my favorite residential sections of Intown Atlanta is in Southwest Fulton, on gently rolling land north of the airport and south of the downtown area - south of I20 and North of East Point. There are 2 neighborhoods in particular, Audubon Forest and Audubon Estates that offer big brick houses on large lots with lots of privacy. These are just ten minutes from the airport, and there are 2 public golf courses within a couple of minutes, plus the golf course at Fort McPherson which will be open to the public after decommissioning in 2012.
The schools aren't so great in the area, but it's loaded with unique houses for less than $400,000, private, nice neighbors and lots of cheap golf.
Best wishes in your search.