Free: Contests & Raffles.
Whitetails will be a tough order on the westside. What weapon choice?
In all seriousness there really isn't a hunt able population of whitetails on the westside. You will have to go East and then go east some more. Blacktails are what you will find here on the westside. Whitetails and mule deer in the middle and a mix of whitetails and mule deer on the east.
Good whitetail hunting can be had in the northeast corner and the southeast corner of the state. Start looking in GMU's 113, 117, and 124 in the northeast. Tucannon river and dayton area produce good whitetail deer in Southeast Washington; GMU'S 162, 166, 175, etc. In the blues you had best wear your kevlar hunting vest because there are a TON of rifle hunters. Northeast part of the state has less people but is much more thick. Good luck in your research!.
There's no whitetail around goldendale. The deer in that area are a cross between mule and black tail.
I would hunt north of Spokane. Most land in the SE is private and land owner permission can be difficult to obtain. The Tucannon River area is nearly 100% private. Most of the "once hunt-able land" has been leased to Broughton Land and Cattle Company. Only their employees are permitted to hunt. Dayton also nearly all private, but you can hunt the national forest. I have been told the Goldendale area south of Yakima offers some great white tail hunting, which is open to the public. I have never hunted there, so you will want to do you research.