In late May, you'll still be limited to low elevation river valleys, whether in the Cascades or Olympics. For the Olympics, the Hoh or the Quinault (Enchanted Valley) will be good.
Even in a normal or below-average snow year, don't expect any alpine areas to be accessible that early. We've had a big snowpack this year, so unless we have an unusually warm next 2 months (no sign of that yet!), it will probably be mid-July in most areas before you can get to the alpine areas, unless you don't mind a LOT of snow and the high lakes still frozen.
I'll leave the Sierra to those more familiar with it. I do know they also have a way-above-normal snow pack, though.
Any chance you can postpone a couple of months?