We started out ride on the BGT at Gas Works park. Soon after passing under I-5 we entered the UW campus area and began encountering numerous major construction projects. Detours were poorly marked and we were forced onto busy streets and sidewalks. Finally, around the UW sports complex, we lost the trail completely. At that point we turned around and rode through the campus (this was a nice ride). I suggest bypassing the UW campus portion of the BGT until construction is completed. Instead, go west from Gas Works Park through Fremont and Ballard or start in Bothell and ride south.
Great, easy, paved trail that will take you from Woodinville (via the Sammamish River Trail) all the way to Seattle. Once you get to Lake Washington, there are some great restaurants and pubs that you can make your way to for lunch. The Elliot Bay Public House and Brewery is definitely worth a stop for some of their awesome food (and desert), plus the beer of course is great. Watch out for the huge hill climb to ascend from the trail up to the city streets, you'll probably want to get off your bike and walk it.
Suzanne O. on Burke Gilman Trail
Very nice trail for biking, running or walking. It can get a little crowded on sunny days but still nice. I ride a3.8 mile portion of the trail to get to work, much better than a bus. :)