Basically from Seattle, you're looking at 4 hrs + no matter what. Like everyone said, BC will host the most (options). The White Salmon will be good, though. This year Mt Adams has better snow pack than the rest of Washington.
Suiattle? Not a huge fan, personally. Lots of wood on a class II run composed mostly of small bowling ball sized rock gardens. Find a river somewhere that is more channelized where the river corridor is comprised of larger bed rock.
White Salmon. You can run the standard class III run, and there's a 10' waterfall (Hussum Falls) that is fun to lap, and easy to portage. Also, above the put in for that stretch is the Orletta section, tacking on a few class IV rapids and a gnarly waterfall you'll most likely portage (BZ Falls)
BC (lots of options, depending on how far you are willing to drive)
but let us not forget Seattle's closest year 'round fix: (only an hour or so away form the city!)
The Skykomish. Perhaps no one has mentioned it because no one is sure what the water levels will be like on it in august this year. We'll have to wait and see. If it is at least 600 cfs though it can offer some fun low water class III.