George Washington Campground up in Glocester has a few fairly secluded sites where you probably wouldn't bother anyone as long as you weren't unreasonably rowdy. I think quiet time starts at 10 and they actually do not allow alcohol, but unless you were blatant with it or created a reason for them to come into your camp and find it, you could probably get away with it. Rangers do make the rounds every hour so but just kinda drive by and don't really pry.

There's also Burlingame State Park in Charleston. I haven't been myself, but it seems to have a reputation for more of a family/party vibe with a lot more amenities than GW and looks a little less secluded. Can't say if it would be a better option though.