Places to see/hear local poets perform their work, and possibly perform your own. Slams, contests, open mics, etc.
Other venues for literary arts, not easily classified...
There are lots of places around town to see published authors read from their works, get their autographs on their books, and possibly even meet and chat with them a bit about their work. I've listed a few below. If you have suggestions for more, let me know!
Seattle has an impressive national reputation for its live theater. Here are a few of the many places around town you can see plays performed live.