if you're interested in Montana, you have a ton of rivers to choose from. All depends on the time of year, flows, experience you want, etc. Freestone/tailwater, big water, small water, remote/less remote, hoppers/streamers/hatches...it's too big to distill into 1 trip.
When I tell people about the state, I divide it into 6 sections
-East: The bighorn, stillwater, Boulder - best based out of Billings
-Yellowstone river & park - base from Livingston, Gardiner, or Bozeman
-SW MT (Madison/Big Hole/Gallatin/Ruby etc) - Bozeman, Butte, Twin Bridges, Dillon
-Central: Smith, Missouri - Helena or Great Falls
-Missoula: Clark Fork, Bitterroot, Rock Creek, Blackfoot - Missoula
-NW: Flathead (south, main, north), Yaak, Kootenai. - Whitefish/Kalispell
Most of the fly shops out there are pretty good at telling you straight up what's fishing and what's not. Streamflow matters there more than you would realize at first. when I lived there, Kingfisher in Missoula, CrossCurrents in Helena, and Parks' fly shop in Gardiner were my go-to stops.
As far as what I'd recommend if you're floating for a couple days, here would be my top choices
1.) the locals prize a Smith River floating permit over almost anything. They're hard to get, but i'm told it's amazing, and truly wild.
2.) The Big Hole. It may be the prettiest valley in the state, which ranks it high up globally. Go in September for hoppers.
3.) The Missouri or Big Horn. tailwaters, similar to fish, biggish water with tons of 15-20-inch fish. Better hatches on the missouri, but both are amazing.
4.) The Yellowstone. Paradise valley is incredible. Plenty of water to fish, good sized fish, lots of tactical options.
5.) South fork of the Flathead. Super wild & remote. Cutthroats/bull trout.
Single day floats on literally any of the rivers can be fun. Boats are the way to go out there. For guides, Walter Wiese at
http://www.ycflyfishing.com/ is great for Yellowstone, the Park, and that neck of the woods. Most fly shops can hook you up with good guides pretty easily as well.