My recommendation would be to get in touch with either the Castaway Fly Fishing Shop (208-765-3133, 800-410-3133, Castaway Fly Shop - Inland Northwest Fly Fishing at its Finest!
) or Northwest Outfitters (208-772-1497, 888-347-4223). Both are in Coeur d'Alene.
I have no affiliation with either of these places but have done business with both in the past. I believe that NW Outfitters is an Orvis shop.
You'll be close to Twin Lakes where the record (Idaho) pike and whitefish were just caught recently, not on flies, but impressive fish nonetheless.
In my opinion, you'll have to drive a bit in order to fish the two better streams in that region, the N. Fork of the Coeur d'Alene River and the St. Jo. Both are relatively easy to reach and in early Sept the waters will be low, unless some afternoon T-storm upsets the flow. We were just there (last Thursday) and drove through a meaningful T-storm just over the divide going into Missoula.
Have fun. It's a beautiful area.
Oh yeah, I almost forgot to suggest if you talk to either of the shops above to ask about the Spokane River, which flows west out of Lk. Coeur d'Alene. I've not fished it, but friends relay impressive data about rainbows there.