Seattle's a great city. I like Sandy's suggestion of going to the Pike Place Market. If you go there, go to the Fish Market on the top floor (street level) for the experience.
If you have time, you may also want to consider going to the top of the Space Needle at Seattle Center. That's a great view of the city!
Seeing as how you've only got a few hours, it's hard to say what to do. As far as luggage storage, I think the Seattle train station has an area for luggage holding. I'm not sure how much it is, but I think it's pretty reasonable, and cabs should be easy to get there when you go back to get your luggage and head to the airport.
2007 - Majesty of the Seas
2009 - Enchantment of the Seas
2010 - Freedom of the Seas