Let the former WA guy spout off a little but feel free to ignore it
September - coho and summer run combination trip. All you need is your striper rod for coho and a floating line for steelhead. Well OK bring some light tips.
What rivers? They're just about all open in the summer and there are king salmon in the tidewater if you want to break your 8wt.
is a tough time to hook up, although there will be fish in the river from the Columbia Tribs from Camas on up to the Lewis, Kalama and Cowlitz; Cascades - Stilly and Sky, and on the OP: Sol Duc will have good numbers as well as the summer fish shooting up the Bogey for the Calawah. Those honkin Hoh summer natives will be gnawing thru surprised angler's tippets and the Elwha will have a few in it's 4.5 miles to the dam as well. The Green has fish through Auburn with most holding up as they reach the gorge until a little later, the Snoqualmie will have a few around but we won't mention where
All that being said I got my first butt-kicking from a bright summer fish on Father's Day almost every summer in my years of bliss out there. You can tie a knot without a flashlight at 4:30am and to get one of these athletes of the supertrout variety in June you need to be there 15 minutes before that at the latest.
Best chances, if you must go in July, would be on the Columbia tribs IMHO.