Orvin, don't confuse anything you read about Virginia, on the STATE level, to apply to anything other than state land. Eg.: those things wouldn't apply to city, county, private, etc.... And only state "park" land, as well (not necessarily other forms of state land).
And just because a place is "rich in relics" (ie.: old and having good potential to find oldies) doesn't automatically mean that a place is a "no-no". Heck, look at the finds forum, and you'll see no shortage of us md'rs posting and boasting of our latest old coins and relics finds, right? Where did you think those guys found those things? At NEW places with no history? Doh
Now if you're worried that other entities and types of land "might have rules" (cities and counties lands in your part of the state), then you can look up those entity's rules for yourself. You know, like if the city or county has a website, and if the muni charter, codes, laws, etc... are listed, you can see if there's anything that says "no metal detecting". If not, well then presto, it's not prohibited

If there's no listing on-line for your intended spot, and if you're still worried and skittish, you can go to the city or county hall, and ask the clerk
"where can the public avail themselves of the listings of the laws, rules, codes, etc..."? (as opposed to asking that clerk "can I metal detect?"). Because ALL laws have to be available for public viewing SOMEWHERE. I mean, doh, laws are not "hidden" and a "secret" afterall. Heck, to be honest with you ... most of us don't even worry or go that far, and just detect.
But once you've done that homework, and deduced there's nothing addressing "metal detectors", you ... uh ... still need to use a bit of discretion. I mean, sure, don't be a sore-thumb digging holes at sensitive obvious monuments. Don't waltz over beach blankets at an archaeologist convention, etc.... We all go at low traffic times, so as not to ruffle feathers. This is admittedly an odd hobby, that draws the curious stares of lookie-lous, and does admittedly "have connotations". So you use due-discretion, and don't be a magnet for attention and scrutiny, waiting for someone to morph something else to apply to your activity.