I went to SW Montana (Big Sky area) 2 years ago in early September, which is a little south of where you will be. It wasn't strictly a fishing trip, but we did fish with a guide one day and got to drift the Madison near Ennis Lake. It was incredible! Lots of quality sized fish (14-16") with a few brutes mixed in that were willing to eat just about anything you throw at them. It's big water and fairly non-descript, so I would imagine it would be tough to wade fish, but I'd recommend looking into a float if you haven't done so already.
The place we stayed in was right on the Gallatin River and I was also able to spend some time wade fishing it on my own. It's loaded with fish, but they seemed to run on the smaller side for me. I spent most of time fishing generic nymphs with good results.
I'm sure you'll have a blast on your trip!