I just got back from Chattanooga and stopped at the track on the way back. I went on down Stringer Road to the Cagle Dairy and spent about an hour with the owners discussing that and the other tracks.
Joel has the names of the tracks correct. The one at Stringer and 140 was called the Cherokee Speedway, and the owners lived right there at the track. Actually, Mrs. Stringer stilll lives there but I decided my hatred of dogs and shotguns meant it was better that I didn't disturb her. According to the Cagles the place was pretty wild, being a race track and drinking every Saturday night before going to church on Sunday morning. The elder Mr. Cagle also said that the local churches were "hard agin racin" (that's "heavy against racing" for those of you not familiar with the south...) and sermons against racing and that track specifically were common.
I took a photograph from the intersection of Stringer and 140, but except for the tree line not much of anything is visible.
I asked them about the other two tracks. The one up by the airport was actually in Ballground, GA in front of the airport. It's now the site of an industrial park. It was called Canton International Speedway or Raceway.

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The track on 108 was a couple of miles from 20 toward Waleska on the east side of the road at this location. The dark area to the south of the small creek was a lake, and the track was just to the north of there. I think I can make out at least part of an oval but it might be my imagination. The Cagles said that they used to deliver milk there for the concession stand, and that one of their drivers took it upon himself to take a couple of laps at speed one night after the racing was done. Unfortunately for him it showed up in the paper the next week.
They also said that right around the time the track stopped running one of the owners was busted for having a still on the property. They didn't remember if that was the reason they stopped running or not.