I'm not a big visitor to tea houses, but two I enjoy are Remedy Tea http://www.remedyteas.com/ and Panama Hotel Tea http://www.panamahotel.net/
What do you like about each of them?
The Panama Hotel Tea is, as noted, in an historic building on the edge of the International District (old Japantown) across from the hillside carved into a community garden. They do have some lovely teas, unfortunately, I am not familiar enough with them to name any. I just select based on a whim or advice from the server. I believe they are served in the heavy iron pots. They also have unusual snacks like matcha pound cake with red beans. The space is just very interesting and there is always street parking close by, metered. You find the parking enforcement guy taking his break, someone taking a meeting, and in the corner, probably someone working on a book.
Remedy Tea is new to me, on Capitol Hill. They have an extensive list of straight tea as well as interesting blends. Also, some simple food including salads and soups, sandwiches and pastries and desserts from some good bakeries. They also have Theo chocolates and nib brittle by the ounce. The space is a little too cool, basement and lots of white, but they do good service in individual glass pots with infusers to be removed when the tea is steeped well. And tea lights to keep the pot warm. They identify which teas can be re-brewed with another pot of water, if you have the time to sit all day (you will find people spending the day at a table with laptop, writing, or I really like watching the guy embroidering (needlepointing?) what looks like circuit board patterns onto muslin. They have good magazines to borrow, a couple of soft sitting areas, a place for kids to play out of the action. And they are responsive if you come in and say you need stress relief, or feel a cold coming, or are celebrating. They have something for every occasion.