Your best bet for an outdoor range is the DNR facility out past Gainesville.
Here are the directions (based on downtown atlanta) for the three DNR ranges I know of.
----------Charlie Elliot----------
Weather Report for Charlie Elliot.....
http://www.weather.com/weather/local/USGA0351
Merge onto I-75 S.
Merge onto I-20 EAST RAMP. go 0.8 miles
Merge onto I-20 E. go 40.1 miles
Take the GA-11 exit, exit number 98, towards MONROE/MONTICELLO.
Go South (turn RIGHT off the exit) onto GA-11,
Proceed to Mansfield go 7.7 miles to train tracks
PAY ATTENTION TO THE SPEED LIMIT SIGNS AS YOU ENTER AND LEAVE THE TOWN
From the train tracks in the middle of town you will travel 2.7 miles to a sign for Charlie Elliot WMA.
Turn left onto Marben Farms road, and the range is 1.4 miles down the road, on the left.
The paved road will turn into a dirt road just before the range.
----------Wilson Shoals----------
I-85 N from Atlanta to I-985 N (to Gainesville)
I-985 becomes Hwy 365 north of Gainesville
From exit 24 (last exit # on I-985) continue on Hwy 365 N 11 miles
Turn right on Mud Creek Road ( gas, food & goodies station at the intersection)
go 1 mile, turn left on Old Cornelia Hwy
go 0.1 miles, turn right on Yonah Road
go 2.1 miles to entrance on left
This is a gravel road and not well marked. There is a large wooden sign announcing "Wilson Shoals WMA."
The range is not marked or advertised, but it is on the right about 0.5 miles down the gravel road.
Estimated drive time is about an hour from the I-285 / I-85 N intersection.
----------John's Mountain----------
Take I-75 north to exit 320 (??verify??) (Resaca/Lafayette/Hwy 136). -- 69.5 miles
Turn left heading toward Lafayette.
You will travel 10.5 miles then you will have to stop at a stop sign.
Turn right heading west on Hwy 136.
You will travel 2/10th's of a mile and turn right at the dirt road.
There will be a sign saying "shooting range". Just go down the road about half a mile, just stay to the right and you will be there.