Campgrounds are hard to find near major cities in the United States. The ones that are may be more of the recreational vehicle (trailers, camper vans, motorhome) type, although I've heard of some that have small patches of grass or dirt that may be suitable for tents. However, I would worry bout someone accidentally backing into a tent. These places may be located at the fringes.
The majority of camping opportunities are in remote locations and usually where a personal vehicle is the usual mode of transport. Especially national/state/local parks and more rural areas near such places. I've heard of some in large cities. The National Park Service has a few in San Francisco (Golden Gate National Recreation Area), but reservations are difficult to get. The other will be more developed in the style of Kampgrounds of America (KOA). Every location is different, but their setup is typically a central building with amenities, showers, etc. The one I visited last included go karts and cabins. This is the closest one to Seattle to give you and idea. The front page has video that looks like it was shot with a drone.
https://koa.com/campgrounds/burlington/
So what are you expecting? Is it festival style camping, like Glastonbury, Coachella, or Burning Man? Most campgrounds have reserved sites that are generally well spaced and have a parking spot or two. Backpacking style where the sites are more or less shared?