If you're in Missoula, stay downtown at the Doubletree. It's on the Clark fork, with wadeable water right there - caught a couple 14-16 inch rainbows in a quick pre-departure hour there last year. If you have a half-day, you could try to book a guide for the lower section of the Bitterroot. Kingfisher Fly Shop always has good info on the Missoula area rivers.
Agree with Freeman that Rock Creek is a good choice, either on the upper end by P-Burg or the lower end by Missoula. I used to work out there, and would schedule a lot of Missoula meetings that ended around 3pm during the summer. You've got less light to work with now, though, so keep that in mind.
As you cross the state on I-90, you will run into a variety of options. Yellowstone parallels the highway, Stillwater kicks in at Columbus, Boulder at Big Timber. At Bozeman, the East Gallatin is an easy stop.
You will cross the Madison and Jefferson as well - those are tough wades at I-90 though. The Clark Fork parallels I-90 from Butte to Missoula, but access isn't all that great.