I used to have friends out in Missoula and visited twice for 2 weeks. I did do some fishing while out there. The Clark Fork runs right through the middle of town, and you can certainly see the trout, and the suckers. They are very wary, and the setting is just all wrong anyway. The Bitteroot is outside of town. It's a very slow moving river, and I never actually tried it so can't say if it's any good.
What was good, and it was very, very good, is Rock Creek. I can't remember how far out of town it was, and it's been 15 years since I've been out there. But it was Blue Ribbon water. I caught a bunch of large brown trout. I'm a terrible fly fisherman but the fish didn't seem to mind and the setting was great. The higher upstream you go, you start losing the browns and rainbows and it turns to strictly Cutthroats. And of course anybody can catch those, they're not too bright. But that's lots of fun too.
It's a long sad story on why I say 'used to have friends' out there. Cancer took one far too young at only 38, and her husband eventually remarried and moved out of State. I've lost touch with him completely.
We also travelled up to Glacier NP, and that was awesome. Not so much for the fishing, although there were plenty of small cutthroats to be had in McDonald Creek on the West side, but the scenery was outstanding, all the way up past the Mission Mountains, past gigantic Flathead Lake, and into the Park area.