I don't recall ever finding one myself, but I've had people with me who found numerous tiny turquoise beads poking around in the small gravel surrounding ant beds. About the size of #7 shot. I think most ruin and campsites in the southwest must have a lot of them judging from the number I've seen people more patient than I am find.
Not sure about places further east, but I'd almost bet ant beds around mound builder sites would turn something, though maybe not beads.
Jack