Mule deer are all over E. WA. The biggest issue is access. You either hunt private land, or you hunt with everyone else on public land. Mule deer are terribly mismanaged in WA. WA allows anyone to buy a deer tag OTC and hunt just about anywhere. The best opportunities on public land, IMO, are special draws out of the regular season, and wilderness areas where you can get away from other hunters.
The wilderness areas are generally clear of snow during the regular season, and the deer will be up high until food and snow drive them to migrate. This means a lot of effort to get to them. Mule deer in the north part of the state will be higher up than whitetails.
The SE corner is mostly badlands and river breaks. In these areas, its the opposite. Mule deer will live down in the creek and river bottoms while the whitetails will stay up high near croplands on the plateaus.