Here is my version of the perfect DuPont day trip. I am sure there are better ways but this gets the big name trails with little back tracking.

Start at Reasonover Parking Area:

Reasonover
Turkey Knob Road
Poplar Trail loop clockwise
Turkey Knob back to Reasonover
Reasonover
Camp Summit Road
Airstrip
Barn Trail Road
Bridal Veil Falls Road
Corn Mill Shoals
Burnt Mountain clockwise
Corn Mill Shoals
Big Rock Trail
Cedar Rock counter clockwise
Little River Trail
Corn Mill Shoals
Shoals Trail
Laurel Ridge Trail
Mine Mountain
Back to Reasonover Parking Lot

If its cold you could probably drop the Burnt Mountain/Cedar Rock portion, there is a pretty tough stream crossing. You could probably also drop Turkey Knob, I find its pretty easy and a good warm up... This will give you about a 15-25 mile loop.

Please share other routes.