Any time from mid May to mid September is good.
It really depends on what it is you want to do and see. If fishing is high on the list, you need to look at the timing of the runs so you'll be there for the peak of the salmon species you want to chase. Typically the best weather in the majority of the state is going to be the first two weeks of July, but weather is never typical. I told my brother that for his first trip, and he just came up for a few days over the 4th. It just so happened to be the summer with warmest driest weather on record, except for the time he was here
Here's a way to look at timing. Mid May we start to green up at sea level, later in May at higher elevations, weather is still on the cool side. June the salmon start showing up in the rivers in bulk, the weather is warmer but it can be a wet month. July is typically your warmest month, fishing is in high gear on the ocean and in the rivers and basic hustle and bustle with tourists visiting and residents chasing fish. August the weather starts to get wetter and a bit cooler, early run salmon are done but the silver fishing is still hot. Late August in the interior leaves start turning color. September tourists are gone, fishing is slowing down, leaves are turning color and the kids are back in school. Weather is hit and miss in September, you'll definitely have rain but the storms seem to run through in waves with nice weather in between. Fishing is starting to dry up.
