I will write about food soon enough, but eating and cooking are some of my favorite hobbies, so this definitely counts as an activity. Seattle is an awesome place if you like to eat.
Culturally, Seattle is excellent. There are lots of shows, and the new downtown library is a must see if you come here - it is like something out of Harry Potter. If you are into music, Seattle gets a lot of artists - everything from small, independent (and sometimes free) shows to big names. A good friend here recently went to a Video Game Music concert at the orchestra and absolutely enjoyed it.
Overall, I tend toward the outdoorsy aspect of activities (such as rock climbing and hiking), but I am really excited to try something new this summer. Look out for updates!