I'm not sure about this, but given the distance from Seattle-Tacoma International Airport to Downtown Seattle, I'm not sure if there are courtesy shuttles.
As far as geographic location that you're looking for, the Quality Inn and Suites - Seattle Center, and the Comfort Suites Downtown / Seattle Center, are within walking distance to the Seattle Center Monorail and Space Needle.
Also, you may want to consider posting this in the "Embarkation ports, hotels, and transfers" thread.
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