Shell Gas Station by the Space Needle
Skyway Shell Gas Station
FREE AIR with fill-up only
Free Air at Chevron
Any Les Schwab will fill your tires for free during business hours. Just drive up to the garage and ask. Les Schwab also repair your flat tires for free, if it is caused by punctures.
Any gas station you come across that has a "Airserv" air/water machine, the clerk can start it for you. They're lying if they can't. Airserve as a company gets all the money put into their air machine, so the gas station doesn't get any benefit except providing the service to their customers. Typically the clerk could start air/water for somebody if they come and ask.
One best way is to simply buy a manual air pump for bicycle, and use that to pump gas into your car tire. Works, also very good exercise ;-)