I know of no Hotel with free shuttles to cruise terminals. It is about a 20 minute drive (no traffic times) to the two separate cruise terminals. Taxis can be expensive given the distance.
There is not much to do near Seatac Airport. The rooms are cheaper at the airport but there is a lot to see downtown. You might be much happier downtown near many of the super attractions like Pike's Market, The Aquarium, Space Needle, etc.