I don't know of any bike shops in/around the Lower Queen Anne neighborhood where Seattle Center is--there used to be a Counterbalance there, but they've closed. I think Elliott Bay Bikes is probably the closest/most walkable option (it's probably a little less than 1.5 miles away).
2009 BMC Road Racer SL 01 / Specialized Ruby 155
2007 LeMond Reno / Luna Chix Team Saddle
1980-something Lotus Odyssey / Brooks Finesse
1992 Bridgestone RB-2 / Brooks B-17 Imperial
Nada Bike singlespeed / Brooks Team Pro in white