Mass Transit from Seattle Airport to Downtown
It is possible to get from the Seattle airport to near your hotel using mass transit. The Central Link light rail travels between downtown and the airport every 7.5 to 15 minutes, depending on the time of day. http://www.soundtransit.org/Schedules/Central-Link-light-rail
If you go to the Westlake stop, you will be within walking distance of many downtown locations, such as .3 miles to the convention center. It would be about a .5 to .7 mile walk to the Springhill Suites, though. If you are staying at the Springhill Suites, you have the option of using the Pioneer Station stop instead then catching bus 25 at the corner of 3rd Street and James, and exiting at Howell & Yale.
If you will be going straight to the MOHAI tour, then exit at Westlake and switch to the South Lake Union Streetcar for the 8 minute ride to the Terry Street stop.
A single ride is $2.75. If you are transferring to a bus or to the streetcar, then it will be $5 total.
Plan your trip here: http://www.soundtransit.org/Trip-Planner