For Western Washington you can only get 1 in the spring season (April 15 to May 31st) only. You can also get 2 in Eastern Wa in the spring season, 3 in the early fall season, and 1 in the late fall season ... note: that both fall seasons are only in Eastern Wa only and you need to see what units are open for number of birds and what sex. I would suggest Colville (Turkey Capital of Washington), Kettle Falls, Chewelah, etc areas of Stevens County (Ferry and Pend Orielle Counties not bad either). Lots of public land and many private land owners will let you hunt when asked.
As for the Western Wa spring season, I would do some scouting (ie - a lot of walking looking for sign) in the Skookumchuck Reservoir area (Bloody Run, Thompson Creek, Upper Newuakum, etc).
Good luck ....