It's not in Seattle proper, but it is between Seattle and Vancouver, so if you don't mind making a little side trip off of I-5, I recommend Xiu Xian Tea, in Kent, VERY highly--she has some amazing teas, including several varieties of high mountain tie guan yin, and does tea tastings for anything you might be interested in. http://www.xiuxiantea.com/
As far as Seattle proper, the New Century Tea Gallery in the International District has some really nice stuff, including some new 2011 harvest greens. And of course, Floating Leaves is excellent.
I'm not as familiar with Vancouver, and have only managed to visit one tea shop in Portland so far--the Tao of Tea one in the Chinese garden--which left me rather underwhelmed. Beautiful garden, gorgeous surroundings--lousy service and so-so tea.