Climbing Queen Anne Hill
A. Coming from downtown, heading north, there are two main routes: Taylor on the east side, and Olympic/10th on the west.
10/27/2010 Update: the bike lane up Taylor is now complete as well; this entire route is now marked all the way from Mercer and Taylor to Boston and Queen Anne.
View Bike: Queen Anne Hill (via Taylor) in a larger map
Olympic/10th Ave route
View Bike: Queen Anne Hill (via Olympic) in a larger map
B. From the east side, the simplest way is to ride the sidewalk along 99 until you reach a through street like Highland and connect to the Taylor route. However, for the adventurous, there's a quick way, the small trail that connects the Dexter turn-off from 99 to Taylor & Crockett. You probably will have to walk your bike, but it can be ridden. Here's what the entrance on the top of the hill looks like:
A picture looking down the trail:
And one looking up: