Don't ignore the State parks out west. There are a lot of them and most are good to excellent.
In the immediate Seattle area, I'd recommend Lake Pleasant in Bothell. We haven't stayed there, since we lived in Bothell for about 17 years and are still only 75 miles away.
Lake Pleasant is about 20 miles from downtown Seattle, and there are few CGs any close because of the cost of the real estate. The good thing about Lake Pleasant is that Metro Transit has fairly regular service to downtown, with a stop right outside the CG gates. Sure beats fighting the downtown parking mess.
If you're planning on going to places like the Museum of Flight, south of downtown, it's not as easy as the central core when travelling by bus.