Hi Adrian. Gregg's Geenlake Cycles is a great shop with every level of bike, and everything else. They are at the east end of Greenlake. Aurora Cycles (owned by Gregg's also) is at the west end of the lake, not as big, but still very good.
Elliott Bay Bicycles on Western Ave north of Pike Place Market, Downtown is a small shop, but they sell an awesome bike
avidson. Unfortunately they are custom made, so if you have time...do it! They do have a lot of Bianchi and other rides too.
Velo Bike Shop on 11th on Capitol Hill is a great shop also.
R & E Cycles in the U-District has some beautiful machines, too. Rodriguez is their specialty.
There are a few more around, but those are probably the best in the downtown, Greenlake, University District areas (you didn't mention the U District, but it's close to Greenlake).
Godd luck!!!
Peace
Cam