Another poster mentioned Prince William Forest National park, and I agree.
It is rarely crowded there---I used to hike it at least once a week during the summer and I would literally go hours on a Saturday morning without seeing anyone else. I saw lots of animals there, including a beaver that chased me!
You mentioned that you wanted it to keep you occupied for half the day--so if you want something else to occupy the other half, it is just down the street from the Marine corps museum.
http://www.usmcmuseum.com/index.asp
This is a GREAT free museum with plenty of free parking.
If the weather is nice bring a picnic--there are picnic areas at the National park and also near the parking lot of the Marine Corps museum.