early June in the PNW

A limited number hikes are available in early June in the PNW, because they need to be relatively low elevation, or else you need to plan on the trails being entirely buried under consolidated snow above (roughly) 3500 ft. A two weeks continuous duration hike just isn't in the cards in the PNW that early. A one week hike might be possible, if you did some messing around instead of trying for big mileage.

If the OP is interested in the PNW, some of the best hikes in early June would be on the Olympic Peninsula in WA, or the Wenaha-Tucannon wilderness over in extreme NE Oregon. This year the low snowpack in southern Oregon might allow earlier-than-normal access to the Kalmiopsis or Red Butte wildernesses, but winter isn't over yet and the snowpack could still change quite a bit by mid-April.