Hoss, Council/Cambridge are good areas, for both deer and elk. Have elk-hunted up there. Did you ever hear the story about the 2 guys that were deer hunting, horse-back, shot a buck and then couldn't find their way back out in a snow-storm, killed/gutted their horses and snuggled inside them for an overnight stay? That was a bad, true story!!
Shoshone . . . there you go into the more eastern part of Idaho, and into bigger Mulies.
Don't know if it still exists, but for a number of years there was a pretty good ML elk hunt just out of Midvale, ID. Me and another guy drew up the hunt proposal presented to (and adopted) by Idaho F&G for that area. That's where I shot my first elk.
We also hunted ML up in the Lowman area, and at that time, you could hunt either sex Mulies and cow elk at the same time. Units 35-36, if I recall correctly. Same guy and I presented that one to F&G, too.
Wolves have wrecked a lot of the elk hunting in Idaho now.