I'd go August/September. It can still be rainy in July and buggy. By August the bugs are dead and the weather is more stable. The rains don't generally come until October/November so September is usually great.
From the middle of July to the middle of September the weather in Portland and Seattle tends to be fair--morning clouds in Seattle. On the Oregon coast summer weather tends to be cool unless there is an east wind blowing--often in September. At Mt Rainier most years the snow level would be ok for hiking around the end of July--give or take depending on the winter. The problem with September is that the wildflowers are likely to be done for.