Ft. Flagler is very good. Beautiful park and setting. Both SP's mentioned are quite a jaunt from Seattle if that is a goal.
If it was me I would stay over on the Olympic Peninsula as you are at Ft. Flagler and make an early AM to late PM day of it by driving to Bremerton, parking the vehicle, "walking on" the ferry to Seattle, and messing around the Seattle waterfront/downtown area. Plenty to see and do. Make a day of it. Pike St Market, Safeco Field (Mariners)/Century Link Field (Seahawks). Ask directions to the monorail from downtown to the Seattle Center and the Space Needle. Plenty of touristy stuff to do in that waterfront/downtown core for one day.
Then take the ferry back to Bremerton to your RV and go explore the Kitsap and Olympic Peninsulas. That could take you a week and you won't be slogging around and through Seattle traffic.
2011 Chevy 2500 Duramax diesel
2019 Timber Ridge 24RLS (Outdoors RV)
Go Cougs!