I went a few years ago. We made it a little longer trip, but what we did was fly to ATL and drive to the RTJ Golf Trail facility in Auburn, Ala. (about 2 hrs from ATL). We stayed there and played 18 Thursday afternoon, 36 on Friday, 36 at the RTJ facility in Prattville on Saturday and we got rained out for our 18 on Sunday morning at Auburn.
At that point, we drove up to Atlanta and stayed near the airport. On Monday morning, we got up early and made the drive over to Augusta -- with the obligatory Waffle House stop along the way. We drove back to the same hotel after the day at Augusta (meaning we could leave all our stuff in the hotel), played 18 in ATL at an average private club the next morning and few out Tuesday night.
Obviously the golf wasn't as great as it could be other places, but it was a good trip that wasn't too expensive. We paid normal rates at RTJ and the hotel in Atlanta wasn't jacked up.
My advice: Make car and hotel reservations now. Those can always be cancelled. The closer you get to Masters week, the more expensive they are.