Where I grew up, we have a really awesome bike trail called the Burke-Gillman Trail (it recently went through major renovations). Damn thing actually runs from Kenmore (possibly as far north as SE Bothell) down into Northern Seattle. I think it travels far enough that you can easily find your way over to the UW Campus once it ends. I believe they plan to extend it far south and north, meaning you could pretty much ride from the UW-Bothell campus to the UW campus.
Some people can actually rely on it for commuting to work, although mostly it's just students. However, even something like the BG Trail is not all that practical. It's great for leisure, though, and runs right in-between Bothell/Lake City Way and Lake Washington.
they also had one in marymoor park in redmond (don't know if you have heard of that place) that runs all the way into seattle. it was awesome.
seattle is probably one of the most bike friendly areas