The Wallowas suggestion is good advice, if you don't mind some miles. (3 hours away).
It will be worth it. Maybe on a long weekend too, to gain another day.
Maybe go up the Tuccannon toward the Blues.
Or up the Touchet toward Bluewood.
(Trying to keep you somewhat close so the drive out and back isn't a killer.)
There are lots of paved campgrounds along the Columbia, Snake, etc.
but they are going to be just as hot and crowded (in my opinion) as camping in Tri-Cities.
Have fun.
