Agree that flies need not be sophisticated.
Meaty streamers as mentioned above.
Stimmies are great as indicator flies or fished alone. They can look like hopper and/or salmon flies. Also tie some of those bigger foam flies with rubber legs for the same purpose like
these.
Rubber leg stoneflies and nymphs also work well too
here. A simple pattern is a
Girdle bug (called a rubber legs out there) it's just a chenille body with rubber legs.
For dries a PMD is pretty much a sulphur and a BWO / Baetis is tied the same as in the east.
Last year a
purple haze dry fly seemed to work well out there. It's a different pattern in the East, but out there it's essentially an Adams tied with a purple body.
If you're more of a hatch matcher, here's a
Hatch Chart for the rivers in the area.
Since you have two weeks, I would sample a whole bunch of rivers/lakes in both the TNP and YNP. Check on flow and conditions when you get there and talk to the fly shops about where to and how to...
Enjoy your trip and be sure to look up at the scenery when your out on the water...it gorgeous! Enjoy!