The Perennial Tea Room is in the Post Alley right by the Pike Place Market, and has a good selection. They have lots of great teaware, and they offer a tea sample of the day. Perennial Tea shop is also located next to some fabulous restaurants and other stores.
This is a wonderful tea shop. The people are so warm and friendly and more than happy to answer any questions. They also give out free samples of any tea that you are curious about. They provide excellent service, answered all of my tea related questions, and have reasonable prices. :)