Chris... I'm in Richmond too (west end, near Regency Mall).
The others on here are right - there are dogs all over the place. It almost seems like they run 24/7.
It can be both a blessing and a curse... If you play it right, they will let their dogs run and the dogs will run a nice deer right to you - heck right directly to your treestand! But then again, you have to put up not getting a good shot or an impossible shot, because the deer won't stop to allow it.
I go out to the GWNF where they don't run dogs. It's peaceful, quiet, and you can go in so far and in so deep, you'll need a compass or a GPS to find your way back out! The only problem is being in the right place at the right time. Sometimes you can be in the GWNF, and not even see anything all day long - not even a squirrel. But with proper scouting, you can be right there and nail a really nice buck.
Anyway, as far as hunt clubs... I don't know of any archery clubs around Richmond. I'm pretty sure most clubs are dog clubs anyway, and not exactly my style, but it's cool... I just hunt where they don't run their dogs. They do their thing and I do mine.
There is a big hunting club up around Fredericksburg called National Sportsman's Association. They are pricey, but they are pretty good from what I hear.
http://www.nsa-inc.com/