I assume from this question, you're new to the area and maybe to Va. Jimmy, so I'll apologize for snapping at your rifle post. The timing was bad and I thought you were trolling.
I doubt you'll find a 24 hour shooting range anywhere down there and late night is a relative term. There is a gunsmith in Matthews which is not too far that may let you shoot late night. He isn't a very good gunsmith and I expect he needs money from any source, He's the only one in Matthews so he won't be hard to find.
Other than that, I can't think of anyplace.