Dash Point State park is about 20-30 minutes away from I5 at 320th S plus the drive into Seattle that generally takes about one hour from down here as an average. There has been an issue with homeless at the park living in both Dash Point State park and Salt Water State park moving between the two. Not sure what it is currently.
Alternate thoughts - there are several concrete parks in Issaquah adjacent to I-90 with a straight shot into Seattle. There is also a KOA in Kent with quick access to I5 near the Kent Boeing Plant.
Lots to see and do in and around Seattle - Seattle is not RV friendly. Museum of Flight, Pike Place Market, Seattle Waterfront, the Ballard Locks, Experience Music Project, Waterfront Boat tour, Seattle Art Museum, Wooden Boats Museum and so much more.
Port Townsend has a park at the point where you can watch ferries and ships coming and going. Fun town to walk around. Lots of choices of where you might like to be
Lake Pleasant RV park gets great reviews. A little bit farther north in Marysville you can stay for free at the Tulalip Casino in a lot behind the casino. From there you can do Anacortes, Deception Pass, Whidbey Island, catch a ferry to the San Juans to Friday Harbor for lunch and then back. Love Washington, just not Seattle traffic so much anymore...........
Long time RVer and lifelong WA resident. Feel free to PM if I can answer any questions. Live south of Seattle as an FYI. Enjoy our beautiful state but don't tell anyone else!