You can fish for trout out there you just have to have a North Carolina license. Stone Mountain is free access
You can keep seven trout per day only in the summer off-season. Starting in October it's catch-and-release only on the main trout stream. There are stream markers nailed to trees all along the creek which note all the fishing laws like when you can and can't use live bait, as well as what months you're allowed to keep them. Be warned that the Rangers do check on people keeping fish when they shouldn't be, and Wildlife likes to drive through, too. It's free to enter the park, but there is a military discount if you were going camping there.
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