I know where they are, but i havent hunted them. They are not plentiful in Thurston, but there are some around. If you go to johnson creek road, which will be on the left side of the hwy as you are leaving rainier towards tenino. Just beyond the bridge that crosses the deschutes on the left is johnson creek raod. you will be able to find some on the wheyerhauser roads up there, you will see the gates. If you go all the way down to skookumchuck road, then turn right, go about 3/4 a mile or something on the left will be thompson creek road. There are turkeys down there as well, with streaks of public land around much private. there are some weyerhauser roads down the road and to the left. I dont know any good places aside from that as i have never targeted them back there, but have come across them when chasing deer. Be prepared to see alot more people then turkeys, it gets rediculous back there..... i drive past it when going fishing, and there are rigs everywhere.
Good luck. hopefully this helps.
(one other thing, bring your steelhead gear, as if the turkey hunting goes bad the skookumchuck is at the end of johnson creek road, turn left and you will see it about 1/2 mile down or so on the right. Really good steelhead fishing in there Tup: ) when its good