Looks like the weather in W. Washington should be okay for the next few days. It is October so you're lucky. It could start raining at any time and stay wet and gloomy until April.
The norm up here is that you normally have a better chance of non-rainy weather east of the Cascades and there are plenty of great campgrounds over there. Wenatchee Confluence SP and Lincoln Rock SP in and near Wenatchee are a couple of our favorites. By sticking around into the Fall in the NW you'll find that rain is the norm west of the mountains and pretty soon it'll start getting cold with frost east of the mountains. Pretty soon snow will hit the mountain passes.