Obviously Yellowstone deserves 'Must See' status- as well as Grand Teton N.P.- Glacier Park isn't too far from Kalispell. It's not easy going, and far from direct to get from Boise to Kalispell. You'll see McCall, ID, and follow the Salmon river for a while if you go up the West side. Some of what you see will depend on the route you have planned- and one is not necessarily better than another- just different. There is this giant (state sized) area we call the 'Primative Area' in the middle of Idaho and you have to either go around the East side, or the West. Both sides are fairly sparsely populated and remote- towns and gas can be few and up to a hundred miles or more in between. Do not expect widespread cell coverage except on major roads. Around the East side, there's Craters of The Moon, Arco and a tour of the first nuclear reactor at Idaho Nat'l Laboratories where many naval Nuclear Reactors are built. As well as the two parks I mentioned at the top.
Keep me posted when you are around Twin Falls, there are a couple of pretty decent restaurants on the Snake River canyon (the 486 foot deep canyon Evel Knievel attempted to jump, and 'daredevils' BASE jump off the bridge every day (the highest legal- and open- bridge in the world where this is allowed). We've been known to meet up with TUGgers if we are around.
You're going to be seeing a LOT of country. Travel safely and enjoy it.
Jim