I have found in my travels in Montana that the rivers "the famous ones anyway" are over rated, crowded, and at the time of year you are going washed out. On the other hand, if you have a float tube you can get into some of the best trout fishing in the world. Why I am telling you this I don't know... If you want a place that is as pretty as any on earth, has fish that will knock your socks off " all wild" and is never very crowded, give Wade lake a try. In that general area, you will find all kinds of things to do. You can take the wife into West Yellowstone for a day, you can go into Idaho and take a look at the Henrys lake/ Island park area. After that head on over to Jackson hole and take a look at the Tetons.. outstanding..

This area of Montana/ Idaho can be really fickle at that time of year. Back in my fly fish or die days I used to haul my wife to places where it was all about fishing regardless of the weather and turned her into a crying mess more than once. She never really minded the trip I have outlined for you however because there was always someplace close by that was "about her"... Good luck whatever you decide !!!
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Clearwater/Salmon Super Freak