Maps of many local trails can be found here. http://blog.2sparrows.org/2009/12/31/trails-of-chatham-county-briar-chapel/
There is parking for the trail along a side street, I believe it's the second street on the left after you enter the main entrance (from 15-501) of Briar Chapel. The street is called Catullo Run. Turn left on Catullo Run, and parking is almost immediately on the right. If you walk a bit further up, along the main road, not Catullo, rather than entering the trail, I believe there is a large posted trail map.
As far as the Southern Village trails, I have gone with the kid before, but they're not really worth going back. I go to Briar Chapel with and without the kids (they don't mind the challenge of the hills, and they can handle a 2 or 3 mile walk). We also head into Chapel Hill occasionally and walk at Cedar Falls Park (on Weaver Dairy Road) or very rarely at Umstead Park (the Chapel Hill one, not the other one). They love to travel to Hillsborough to hike at Occonneechee Mountain, too, but that doesn't happen very often because it's a trek just to get there.
The trails at the new(ish) Rock Ridge Park are fine, if you like paved walks, but they're definitely not my favorite, and I'd only go there with kids, and only if it was too muddy to be out on real trails.
The humor in all of this local trail knowledge I have is that we live on 9 private, wooded acres, with not a single trail. We need to get working on that. Someday. I've been saying that for 12 years.