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Welcome to the forum. No one is going to give you a specific answer since grouse hunters work hard at finding good spots.They will probably be willing to give you suggestions regarding books, youtube videos and WDFW biologists for help and might give general areas of the state to head for.Good luck and hope you are successful this Fall.
As Oldguy stated, GOOD grouse spots are protected by a lot of hunters. With that said, there are plenty of options in King County to go explore and get on some grouse. If you can find some gated roads just start walking them during the season. I am far from a serious grouse hunter and have had 100s more scare the heck out of me than I have killed but l find a lot in areas where there are fresh berries and good cover. Keep your eyes peeled not only in the trees but also along the edges of the roads as they love to sit there during the day, just waiting for their time to flush and test your bladder control.