Only when all other options are expired..
The UW campus, like any major state school, is truly admirable in an antiquated sort of way. If anything, go there for the architecture - you won't find similar-sized Gothic buildings anywhere else in Seattle! Try to make it in the spring when hundreds of cherry blossoms are freckling the campus' main lawn. During the spring/summer there are quite a few worthwhile festivals and bazaars taking place on University Ave, right outside campus.
Keep in mind that the UW campus is NOT a huge tourist attraction, though! Go see the real sights first...