It's exactly an hour from my house I believe (I live at the crux of I285 and I85). It's a straight shot up I85, to I985, which you stay on all the way up to Clayton (it changes names a couple of times but it's basically the same road - no turns). From where you live, there's probably a much faster route. You should bring the dogs - last year Lori brought hers (there are no park rules against them - and they would probably enjoy the woods!)
The park is located right in the corner of the state where the Carolinas and Tennessee border, due north. There's a path going up 400 but I'm not sure about it.
-- Best, John