well, I mentioned other parts of Henry's Fork, which IMO, were better fishing than the famous spots. At least if you want to actually catch decent numbers of fish. The problem with those other areas is that there's only a few spots were wade fishing is productive, best in a drift boat, and I didn't have a drift boat.
I agree if I had total choice other rivers would come first. I'd pick out a nice, mountainous area without all the hubub of fame. Gross Ventre Wilderness, Teton or Shoshone National Forests, or somewhere in central Idaho in the River of No Return area. And that's just Idaho/Wyoming, I don't know Montana all that well. Pick out a good looking random blue line you've never heard of, away from roads, with some interesting tribs here and there. Pack camping gear for a long hike. Spend a day hiking in, set up camp, do a lot of fishing, hike back out.
But in many cases it's merely a matter of time. I was based out of Idaho Falls for work reasons and, generally, taking day trips. Day trips suck if you gotta go several hours to get there and several more to get back. And thats real common in the west, there are good areas with lots of good fishing, but they may be hundreds of miles from any real civilization. So the only way you ever actually get to fish them is to devote a multi-day trip for the sole purpose of fishing. Nice when you can do that, but it's not like you can just decide to go fish for the evening after work. The good streams take planning. The famous ones are famous because they don't, they're closer to actual people, rather than being better fishing.