Seattle, Washington

Not many good choices near Seattle. We have stayed at the KOA in Kent WA a few times not bad but spendy. That was the closest we could find.

Millersvania state park about an hour south

Hard to beat Lake Pleasant RV Park in Bothell. Small town feel yet close to I-5 and even closer to the 405. I used to take Bothell Way and then skirt Lake Washington all the way in to the university district which is a hop and a skip from downtown. In my opinion, the key to traveling in Seattle is being in a place that affords multiple options... Like Lake Pleasant.

Since this question is asked all the time, there are hundreds of posts recommending Lake Pleasant as the best choice.
It's recommended way more than any of the other few options.

Most every Indian Casino has camping The Tulalip In-res, in Marysville is really nice and is about 45 mi drive to down town.

Few choices even close. Kent KOA is basically a parking lot but easy access to get into Seattle, 30-60 minutes. Lake Pleasant is north and likely an hour into town given traffic. Two poor choices in Issaquah but location to town not bad. All would work for sightseeing.

KOA Kent is good but it's across the street from AMAZON and a lot of part time workers.

Lake Pleasant is the go to for most. It's easy to get to the freeway, convenient to restaurants and grocery stores (walking distance).
Very nice and quiet.
If you go there, ignore your GPS and DO NOT turn until you see the resort.

The very best way to explore Seattle is to stay on the Olympic Peninsula side of the water (Port Townsend, for one) and drive down to get on the Bainbridge Island ferry, park the car and take the fast ferry to the Seattle waterfront. It will let you off near the Aquarium and Pike Market. You can also get on a quick monorail and soar over the city to the Space Needle. Shop at Pike Market before you leave for the day, board the ferry and relax. You could even do it 2-3 times during your whole stay and it would be so much more pleasant than staying in Seattle, finding parking spots and fighting traffic. There is a lot to do on the Olympic Peninsula in beautiful surroundings.