Aaron's in West Seattle is very commuting culture oriented.
Gregg's is always popular and is where I bought my first real bike (Schwinn Varsity) back in 1973.
Counterbalance has 2 locations, one downtown and one on the Burke Gilman Trail not far from the University of Washington. Really top notch shop.
Elliott Bay is a great shop, and I believe you'll see some Davidson bikes on display there (I'm pretty sure they are still the home of Davidson Bicycles).
Bothell Bike and Ski is north of Seattle (Kenmore/Bothell area); great guys and a complete bike shop.
The REI flagship store is always an interesting place to stop. I'm a little biased towards independent dealers, but I have spent money on bike stuff at REI.
This list just scratches the surface.
My favorite place for repairs is Perfect Wheels on Roosevelt. Very small shop, but Larry is a master.