Pilgrimage to Mec.. I mean Seattle

Work is unexpectedly taking me to Seattle next week, so of course I want to check out a few coffee spots. I imagine I'll hit the original Starbucks just to say I did. But where should I go for the good stuff? I live in NYC, so it's not like I don't have good coffee locally, but there must be some interesting stuff in Seattle we don't have here. Up for any suggestions. Thanks!

ED: Thanks for all the suggestions everyone! I think I've got a good list of places to check out now.