There's nothing on the North American continent that the 30-06 isn't capable of handling. You should be good to go unless you just want something else, and there's nothing wrong with that, either!
Go online to the Washington State's department of natural resources (it may be called something else) and research the game laws and public hunting areas. There may also be local forums that can steer you to hunting clubs or recommendations for public lands as well.
It's a beautiful state with lots of good outdoor opportunities. Enjoy!
XD-40 service, XD-9sc, member GeorgiaCarry.Org, National Rifle Association, Gun Owners of America, North American Hunting Club, Rocky Mountain Elk Foundation