Check out the "Ranges" sticky at the top of the Virginia hometown forum for some of the ranges and info.
But you'll find as others have noted: only semi-local range (other than finding someone with private land willing to let you shoot on it) that has 300 yard (I believe - don't know if true 300m possible on it) is the C2 in Va Beach/Pungo, and that's still a good hour away.
If you're willing to drive a couple of hours, then Quantico and Cavalier come into consideration. Quantico is north of Fredericksburg, and Cavalier is west of Richmond in Montpelier. I was interested in joining the Quantico club as they were recently accepting applications, but unfortunately we're outside of their membership radius (75 miles IIRC?). Cavalier is not listed in the above-mentioned sticky - it currently has a 500 yard range, and I've read has recently received county approval to expand that to 600 yards. Usually very lightly used due to the capped membership, but that cap is also expected to be increased starting next year.