Cavalier is a great club. You'll never feel like a fool out there. Mainly because no one is ever out there, at least not in the clays field that I've shot.
Problem with Cavalier is that you need to be a member, and last time I checked it was a couple years waiting list.
If you can find their web site, find Henry Baskerville's name and number and give him a holler. Excellent old Va. gentleman who will talk your ear off, but he can give you the lowdown on membership. Also, if you are inclined, he is one of the best shotgunning coaches I have ever met in my life. The guy can shoot.
Other places for clays, from Mineral, you really need to go to Old Forge in New Kent County, Flying Rabbit in Harrisonburg, or Quail Ridge in Lexington. I am sure there are others, but those are the ones I've shot.
As for freebie places you can take your Trius, you just need to meet some farmers. There are plenty of people in Mineral with enough land that you should be able to find someone willing to let you throw on their property. Beautiful part of the state, and lots of open land.
Good luck.