[@JackHasAShotgun] Maybe they (The character) fled inland to get away from the intial chaos, and decided to continue west as opposed to all those who were headed back east to find shelter. Cars still ran in the first few, lets say weeks? (I have a reason why cars are harder to come by now.) So, we'll use that to give your character a reason to be on the west coast relatively quickly. Even though they could easily walk it in three months, without water they would die.

However, think of this more as a parallel earth. You don't have to actually know the area too well. The only real big important things is Washington state is known for having Naval Bases, and the national monument, the Space Needle. You can use google maps to get a feel for the layout once I pick an area. Otherwise, it should be pretty simple and forward, we'll make things up as we need to go and I'll document important locale's as needed. You don't have to get so specific as to know the street names. Really just the names of outlying towns and the basic geographical area.