A six-day, 55 mile hike through the Sawtooth Range was probably the best backpacking/fishing combination I ever did. Still, especially for those not used to high elevations, I suggest hiking down the middle fork of the Salmon River in Idaho, about midway between the towns of Stanley and Salmon. This famous stretch of wilderness river is famous for its scenery and teriffic fishing for cutthroat trout. It's usually run by rubber rafts, often with professional guides. But there is also, I've heard, a suitable trail running downstream from Bear Creek, the usual launch point, to the mouth of the Middle Fork into the main Salmon. Research it first, of course. The water should be perfect in September.