What aimless and W_D said!

A few other places in the Pacific NW accessible in June would be the Rogue River Trail and Hell's Canyon. Hell's Canyon could last for 2 weeks, but if you want a resupply you'd have to arrange it with one of the jet boat outfits ($$$). Otherwise, you'd probably be looking at two one-week trips in separate locations.

For California, watch the snowpack because they are actually getting moisture. Everything depends on how long the current series of storms keeps up. The Sierra may hopefully get a bit closer to normal, in which case early June would still be quite snowy.

As mentioned, don't count on fires. I suspect they'll be banned quite early in the year, depending of course on the weather between now and then. Wood stoves are banned when/where campfires are, and there's an increasing move to ban alcohol stoves in dry conditions, too.