Well, for the most part, in eastern Idaho, the nugget hunting is a no go. For coins, you have to remember that this area hsn't been settled all that long, so there aren't tons of coins like back east. Most of the coins I've found have been at old homesteads, and ranches, and mines that were abandoned long ago. you might try getting permission from the owners of old houses up there, or maybe in St Anthony. Also, do some research for amusement places that are now gone, though most of them now have new buildings on the sites, especially in Rexburg. Research is the key to successful detecting.
If you want to hunt for gold, you can pan on the South Fork of the Snake. I don't think there's gold in the North Fork.
Jim