It's just hard to predict in the PNW. It looked like we were going to have a low snow year but March more than made up for any chance of that. June is one of the more frustrating times (at least for me, who grew up in the south) when the THs and access roads are still under snow. I don't mean to be trite with this obvious statement, but staying below at lower elevations (say 3500' or so), farther south (southern OR will be snow-free quicker than northern WA) and/or east of the Cascades will help.
So where to go?
Maybe Hells Canyon in eastern OR, out-and-back trips in any one of the numerous river valleys in Olympic (just have to be flexible about a turn-around point), southern OR wilderness areas (maybe Thom Darrah will have some input here). I'll keep thinking.