Aparently im late to the conversation, but anywho..
I would check the states .gov site. Here in CT any rc planes, drones or uav flying is not allowed in any form at state parks. The whole landing takeoff thing may be a loop hole if your not in the park yourself, but I doubt any ranger here would care or know the difference...
ct.gov{The use of remote controlled model aircraft or “drones” is prohibited at Connecticut State Parks, State Forests or other lands under the control of the Department of Energy and Environmental Protection, unless specifically authorized by the Commissioner in a Special Use License.}
But for your trip heres the Washington info.
http://parks.state.wa.us/1080/Remote-Controlled-Aircraft
It looks like they allow it as long as you have bought a permit for the day. $25 to apply, and may have other fee's. apparently there is also a separate permit if you want to film, or take aerial photos...
I would love to see an episode of FliteTest for new pilots that discusses finding places to fly. Whats legal or not, advice on finding or even starting a club, stuff like that. I'm new to this, and theirs not many clubs in my state, and only one within acceptable driving distance, though when I went out to the air field it was down a dirt road, and at one point crossed a 20 foot wide stream with an incredibly unstable looking plywood bridge. Considering I am not sure if the club is active since their website looks ancient, I decided to reverse back out to the dirt road and headed home. Personally I have been flying (learning to fly) at city parks at odd hours when there is no one around, as far as I can tell that shouldn't be illegal here... not really sure..