Hi Mus50stang,
I live in Vegas. The local club I’m a member of is Gold Searchers of Southern Nevada. They have a claim up in the Johnnie District (just NW of Pahrump, NV), and a few in northern Arizona (by Dolan Springs/Meadville). I believe that Nye Gold Seekers has a claim in the Johnnie District too. I’m pretty sure they’ve also got a claim or two in the Congress District (also by Pahrump).
GPAA, and Mohave Prospectors Association have good claims in northern Arizona. They’re all pretty much in the same area, and all give up pretty good gold if you're willing to work for it.
GPAA has a claim near Nelson, but the area is mostly lode. You might be lucky and find a pocket of placer, but it’s definitely not distributed widely/reliably like the AZ gold fields. There’s also a claim near Barstow.
I’m not sure where in SNV you are, but if you’re in the valley, you’ll unfortunately need to drive 1-3 hours to get to a decent placer area.
Cliff Notes:
Clubs that would have claims you can access somewhat near Southern Nevada -- Gold Prospector’s Association of America, Gold Searchers of Southern Nevada, Nye Gold Seekers, and Mohave Prospectors Association.
If you can and/or only want to join one, I’d go with Gold Searchers of Southern Nevada.