The "best" river diving is near the location of "old" landings. Back in the day, crossing rivers was done by ferry. Small towns or villages near the river with names like Taylor's Landing or Mill Ferry and usually good places to start. Go to the County library or Courthouse and see if you can find an old map. Start with older bridges, they were usually built at or near the old ferry or landing. Locate these spots on the map.
Rivers have a tendency to migrate, especially in the Piedmont. Try and match up the river on a modern map. Old surveyors maps are the best. If you can match it up and find an old ferry or landing go check it out. Find a country store or a post office and ask around to see if anyone knows where the old landing was. If the river is still the same you have a shot.
If you actually find the location, look downstream of the site. if the river is fairly narrow, you have a good chance. Go to the first elbow bend. In the bend, underwater, will be a trench. In the trench, all the loose stuff accumulates. Dig with a ping pong paddle as a fan. You need a powerful light and even then visibility will be near zero.
River diving is DANGEROUS. DON'T dive in current unless you have experience, a back-up diver and a bailout plan. It's easy to get entangled and DROWN. Make certain you have multiple cutting devices in reach of either hand, including a long one to cut behind you. Old bottles, coins and other JUNK aren't worth your life, no matter how cool it might be.
On the bright side, artifact potential can be high. Anything that fell overboard or was dropped can be found. Use of an underwater metal detector can help. Keep in mind, Virginia has laws that you need to check and follow. Don't dive on National Forrest land and not expect to get caught, as well.
Hope this helps...
Andy