Big snow pack up that way. I'd wait until at least late July. Loads of small to medium creeks as well as the bigger rivers. When I fish up there I usually have a good selection of the following flies...
Dries:
Stonefly patterns, Stimulators, Hoppers (yellow and orange), Ants, Beetles, and maybe some smaller mayfly and caddis imitations. For the terrestrials, I'd recommend sizes in the #6-12 range. As for the mayflies and caddis, you might consider going as small as #18.
Nymphs:
Pat's Stones (#6-10), North Fork Specials, misc stonefly nymphs, Princes, Pheasant tails and Twenty Inches. I usually go for bigger nymphs in general but smaller nymphs would be good for the smaller streams. A good range of nymphs would be in the #6-16 range.
Misc:
San Juan worms, leach patterns (pine squirrel leech is a fav), random dries like Renegades, Yellow Sallies and Paralyzers can be good to have as well.
I generally find that tippet size is less of a concern on the less pressured water. 3-4X should be fine for most water but it wouldn't hurt to have some 5-6X for those pickier fish.
In July/Aug the hopper/dropper fishing can be off the charts.
You'll have a great time.