I've lived around RVA a couple of times and comps (let alone outdoor ranges) are few and far between. I'm not sure what's down by VB and Chesapeake or far out west, but it's slim pickings within an hour of the city. I've never lived there long enough to join one of the club ranges (which is pretty much your only option), but the only thing that intrigued me was the open matches at Quantico. Although I never made it to one, I saw a lot about them on VA Gun Trader (I think) and the VA shooting reddit page. I heard Cavalier in Montpelier is the best range/IDPA, but it's a year wait list for membership and I never actually went.
Side note: If you're thinking about going to the public game lands on a weekend to shoot a few rounds or zero, I would highly suggest you don't. Early weekday mornings is your best bet or you're putting your life in some sketchy peoples hands. I had a hankering to shoot one weekend and it was so sketchy I feel obligated to mention it.