The James River WMA is primarily used by hunters and fishermen throughout the year. However, one of the benefits of this place is that it is also open to dispersed campers! You simply need to purchase either a daily or annual access pass from the DWR website and then report which days you will be staying at the WMA--it's currently $23 for the annual pass.
After turning onto Midway Mills Lane from the northern end (route 626), there is a gravel access road about .5 miles down the road that is well-maintained. It almost immediately opens up into an open field where large rigs of any size can fit. There is another site further down the road, but it is smaller and primarily used for truck campers and tents.
This is where we stay any time I need to work in-office down in Lynchburg, VA. It is 20 minutes from the closest grocery store (Food Lion), liquor store, gas station, and propane supplier (Foster Fuels).
I had great T-Mobile service, but no ATT service--even with a powerful LTE antenna. I do not have Verizon so I cannot comment on their service.
This isn't a campsite for the best "scenery" or anything (though it is pretty in the morning), but it is quiet (you might sometimes hear dogs or gunshots from hunters who are near the water-fowl impoundment at the very end of the road by the river), secluded, and convenient. If you need a place in central Virginia to camp for (almost) free, this is it.