aramis erak
Legend
Seriously though, Powell's Books in Portland is only three hours away - last time I was there (about ten years ago) they had tons of RPG books. Can't remember much in Seattle, but haven't been in a decade.
Guardian Games in Portland is a better choice, but Powells DOES keep a large selection.
Did a quick google for D&D Adventurer's League Seattle...
got the following:
https://www.meetup.com/Seattle-Dungeons-and-Dragons/
Also, from them, I found the D&D AL play
DELRIDGE Uptown Espresso and Gameporium
3845 Delridge Way SW, Seattle, WA
Fridays, 7P to 12A
You're best finding a D&D AL group, then asking them... because most hardcore AL players will know of two or more weekly sessions, and often 2-5 stores and their scheduled AL nights. But you can also find players for other things.
For example, I'm a bit burned out on 5E (I know, around here, that's borderline blasphemy)... so I let people, including the store, know that I'd be doing Star Wars with an open game in place of the AL table I'd been running. (We finished Hoard.). I get the same table, half the same players, and 3 more besides, including one new guy, and got myself invited into a Dresden Files game.
And I also have, from the same meetup, spun off a non-public Star Trek game, too. This in a town where the general advice to gamers has traditionally been, "Get used to D&D and Pathfinder, because no one over 18 runs anything else, and the under 18 crowd might also do Rifts...." (This was from a store owner...)