If you are looking for a place near Seattle that is quiet yet not too far out there is the Tall Chief resort near Fall City. It is former Western Horizons Resort now owned by Encore. I haven't stayed there since they changed hands a couple of years ago.But I hear it has been updated a bit. This is the best I know of on the east side. The KOA you mention in Kent does have a poor reputation. Not sure of anything else in the area since we usually are heading in the opposite direction,away from the city, towards the mountains when the trailer is hitched up.
There is a lot of great camping in the Cascades and the Olympic Penninsula if you want some time away from the city. The loop around the Olympic Penninsula is very scenic with lots of places to see in the National Park and along the coast.
In the Cascades, beside the mentioned Mt St Helens, the towns of Leavenworth and Winthrop on the eastern slopes are fun to visit and the drives over the passes, North Cascades (HWY 20)or Stevens Pass (US 2) are not to be missed.
2005 CF29RE 04 Ford F250 crew 6.0 P/stroke FX-4.
(pic coming soon!)