I've been meaning to visit the Experience Music Project museum for some time. Started as a shrine to Jimi Hendrix by Microsoft cofounder Paul Allen, the museum offers much more. I particularly enjoyed exhibits on the early years of Rap music, as well as an in-depth exploration of the history of guitars.
Designers will throughly enjoy two temporary exhibits, on one concert posters allows for great exploration of typography and print-making, while Double-Take counters classic artists like Van Gough to moderns such as Lichtenstein. The museum also offers some innovative computer technology that allows all-ages to get hands on with instruments as well as receive some digital tutoring in musicianship.
The building itself is even a piece of art and is a Frank Gehey master-piece that encourages you to explore. Even if you're not a passionate audiophile, the technology and design aspects of this museum make it a must-stop for those passing through Seattle.