Seattle doesn't have any arcades full of classics; the few that exist are, for the most part, spread around the city in ones and twos.
Shorty's is a bar in Belltown that's well-known for pinball and usually has a few licensed retro-multigames (Ms Pac/Galaga reunion, DK/DKjr/MB, etc.)
Pink Gorilla in the U-District has an arcade in the back that is a mix of new games and older games; i don't know if there's a list on-line anywhere of the current lineup.
Gameworks is loaded with new drivers and shooters but still has a few vintage games upstairs in some back corner in those bizarre custom wood cabinets; usually a few pins too.
Tacoma has a few spots if you're headed that far down south. the B&I on South Tacoma Way has an amusement center with a mix of old and new containing quite a few classics. unfortunately, those classics are pretty poorly maintained and generally not worth going far out of your way to play. there's also the new Dorky's Barcade on 9th & Pacific which i've yet to visit so i have no idea what games are there.
Portland has by far the best arcade in the Pacific NW with Ground Kontrol; it's probably second in the country only to Funspot in N.H. 25+ pins and 75 or so video games, 21+ after 5 p.m. so they can serve alcohol. if you have the time and ability to get there Portland is worth a side trip, not only for GK but also other spots such as Powell's books and Voodoo Doughnuts, all in a small area downtown.