Last minute car rental deals are generally provided from two weeks to as little as one
hours notice. See our Tips on Finding Last Minute Car Rental Specials
I would suggest that a week or so before the rental starts is a good time to start looking for such deals. Of course, you should look more in advance as well.... last minute deals are usually quite restrictive -- ie they may only be for certain cities, certain rental lengths (ie weekend rental only, weekday rental only, max 5 day rental, etc )and/or certain car types (specials on economy cars are the most predominant).
For Seattle, it will probably be less expensive to rent downtown, rather than the airport. Airport rentals are usually more expensive because of the extra airport-associated fees.
The only way to know for sure is to do some rate checking for all Seattle locations for your preferred company, the dates, times, car size, etc.
I hope this helps and I hope you find a good selection of last minute car rental deals in Seattle to choose from!
Pages from this site, relating to this topic:
Comparing Car Rental Rates