Check with the Seattle chess club.
Seattle area chess

Youre welcome. If you get a chance to chat with Viktors Pupols do it. The guy is incredibly nice, and full of chess stories. He actually played and beat Bobby Fischer.
http://www.chessgames.com/perl/chessgame?gid=1044024

The OP started this thread on 10/26/16 You'll be working in Seatle "this summer"..?? Did I forget my medication again?

Youre welcome. If you get a chance to chat with Viktors Pupols do it. The guy is incredibly nice, and full of chess stories. He actually played and beat Bobby Fischer.
Neat game! Of course, Bobby was not famous at that time (He was only 12 years old). Still, a nice memory for him I'm sure.
Here's a link to Northwest Chess with every club in the Washington, Oregon and Idaho. University clubs are mentioned as well.
http://www.nwchess.com/clubs/index.htm
The OP started this thread on 10/26/16 You'll be working in Seatle "this summer"..?? Did I forget my medication again?
Hahaha, I meant the summer of 2017 (some summer internship offers are out now, but I realize it doesn't make much sense outside of that context). Sorry for the confusion.

As mentioned, Seattle Chess Club and NWCHESS run tournaments fairly frequently. Our meetup group has casual chess meetups all over the Seattle area most days of the week so you will likely find something that fits your schedule. You can check the calendar at www.seattlechessmeetup.org.
Hope to see you there!
I might be working in Seattle this summer and was wondering how tournament availability is then. It likely won't change my decision but I had to ask :D