Most states out west allow prospecting on federal land that doesn't have claims filed.
Most all of the gpaa claims are open to dispersed camping for up to 14 days. Weather might make access difficult to some.
If you get to Oregon I can suggest the quartzville group, located about 50 miles east of I-5, halfway between Salem and Eugene, and 25 miles from services. There is also a large public area close by. Usually no snow but can be cool and rainy. Water can be high.
I'm part owner in 2 of the 3 claims in the group, and more than happy to show you around.