Definitely recommend 3 Island Crossing SP. Massacre Rocks is nice but not super-friendly for large rigs. Off the interstate but interesting to visit and a nice CG is Bruneau Dunes SP. Another interesting side trip, should you be interested, is Castle Rocks SP/City of Rocks National Refuge in far south central Idaho; nice campground there (elec-water) and fascinating scenery, but can be very hot in the summer. I'm not sure, but I think the weekday senior rates are available for in-state residents only. If not, they'd be worth considering.
We haven't found a CG we especially like for Boise; we'll keep trying. :) Have heard good things about Mountain Home RV Park but haven't been there yet; that's about 50 miles east of Boise. Could be a good base camp for visiting Boise and Bruneau Dunes.
One CG we also like, great for an overnighter or for a few days' base camp, is Village of Trees RV Park in Declo, along I-84. It's right on the Snake River (and you can fish from there; license probably needed) and despite being right along the interstate, the trees serve as a bit of a buffer and the noise isn't bad, especially in A & B loops. Conveniently located behind a gas station/restaurant. (It's better than it sounds, trust me.) FHUs, nice private bathrooms in the satellite bathhouse. Good base camp for City of Rocks, Twin Falls, Minidoka National Historic Site, etc.
Glacier has a lot of nice CGs nearby and in Kalispell, but you will need reservations in July & August. Large rigs can be quite happy at the West Glacier KOA, which is an exceptionally nice CG, despite lack of shade. For Yellowstone, our favorite for a stay longer than a few days (which the OP plans to do, and is strongly recommended) is Grizzly RV in West Yellowstone. FHU, very nice CG, convenient to town (restaurants, tourist shops) and only a few blocks from the west gate of the park.