If you're just going to be in Seattle proper, here's a few of my favorites:
Big Al's brewing:
https://bigalbrewing.wordpress.com/
Their dark beers, stouts and porters and the like, are pretty damn good if you're a dark beer guy.
Odin Brewing:
https://odinbrewing.wordpress.com/
Their belgian beers are generally very good, and I'm a fan of their amber, which is made with Juniper berries.
Reuben's Brews:
http://www.reubensbrews.com/
Reuben's basically specializes in rye beers, so if you're a fan of a good rye beer, they're the place to go. They're also almost literally next door to Stoup Brewing, so you can get an easy twofer by heading down that way.
If you're willing to head out a little ways, there's a few others I'd recommend.
Black Raven Brewery:
http://www.blackravenbrewing.com/
Located in Redmond, the best brewery in the state hands down, in my opinion, and you're going to be here at just the right time. Trickster IPA and Second Sight Scotch ale are the highlights of their normal array of beers, but their best stuff is in the "Rare Birds". 3-4 excellent and often experimental beers, right now it's dominated by old favorites like Gunpowder Plot porter and Grandfather Raven (which releases Friday, WOO!). If they still have Corvus Frambicus on tap and you like sours, that's a pretty good rasberry sour. They're also almost right next door to Hi-Fi brewing, which does some pretty good stuff too.
American Brewery:
http://americanbrewing.com/
Located in Edmonds right by the ferry. Solid line up of regular beers and their seasonal and experimental stuff is usually pretty good. Just down the road from Salish Sea Brewery, a new place with pretty good dark beers.