I would have to agree with the other recommendations to hit DuPont. There is a great variety of terrain, with some trails being similar to parts of Brown County. For younger riders, I would think it could be ideal.
The Guion Farm trailhead area has a "skills" area, with a teeter-totter and boardwalks to test the younger riders, and leads to some easier terrain.
Ridgeline is a roller-coaster of a trail. If it were around here, I'd ride it all a day long or at least until I got bored. Also, Hickory Mountain was a fun ride. It's a good warm-up climb, followed by a decent downhill. The two can be tied together if you take the right turns.
Also, the climb up Cedar Rock, taking Little River to Cedar Rock is an experience. Riding the slickrock is the highlight. Big Rock, one possible descent has a rocky drop, which could be a little hairy.
Nice plastic-y maps are available at the LBS's for both DuPont and Pisgah, and could be a worthwhile investment.
Bent Creek, closer to Asheville is also an area with kid-friendly terrain.