A lot of people train at Flathead Lake, as it's one of the best bottom compositions around. We have dove in some really silty things out here, and a lot of people make trips over to Seattle even for checkout dives. Having dove in Puget Sound, my husband and I were really spoiled and find lake diving okay, but the aquatic life doesn't compare. Still, it was a neat challenge finding our freshwater buoyancy.
You can get in touch with my husband,
8th Element Diving Home: Scuba Diving Classes, Trips, and Travel, he's an independent instructor and can help you out more. I know he's thinking of teaching a drift course on one of the rivers this summer, which might be fun.
Note that last year in August the rivers and lakes were really low, and we had fires across the whole state, and for a few days in Missoula we had an air quality warning advising us to stay indoors. In September we dove a few lakes and one was remarkable at how far down the water line was. So, I would recommend a backup plan. Flathead is big enough, however, that you will be safe there.
I know you didn't mention this, but if you do go rafting (which is gorgeous by the way) really screen your guides. We watched some of the guides on the Gallatin River have packed boats in August when the water was so low the rafters had to pick up the raft and climb over rocks for half the trip. If you book a raft trip, ask them about the volume in August. I do highly recommend checking out the Blackfoot River, there are shuttles you can take and you can float down in an inner tube. You can also dive some of the holes there as well, though they're not very deep.
Oh, and even though it will be hotter than Hades outside, don't forget thermocline. It really gets freakin' cold with these glacial-fed lakes.