The airport isn't real near the pier. Sea-Tac airport is actually between Seattle and Tacoma, and is about a 15-20 minute drive to the pier (at least) depending on traffic. Off the top of my head, the hotels that will be nearest the pier will be the ones in the downtown Seattle area, such as Homewood or Mayflower Park. Not sure how cheap they are though (having lived in the Seattle area for 6 years though, I can tell you that there ain't much around there thats cheap lol)... I suppose you could also stay in a hotel near the airport, there are plenty and there may possibly even be transport to the pier.
November 2008-Carnival Valor (Miami, FL...Nassau, Bahamas...St. Thomas, USVI...St. Maarten, NA)
February 2009-Carnival Conquest (Galveston, TX...Montego Bay, Jamaica...Grand Cayman, Cayman Islands...Cozumel, Mexico)
August 2010-Carnival Dream!!!!