Watch out for SEA airport hotels that charge a fee (I recall $6 per person) to use their own airport shuttle service. There are a couple hotels that don't look great but are located right across the street from the terminal and hence would be walkable if you don't have a lot of luggage.

The last time I had an overnight connection at SEA (which wasn't a late arrival or early departure), used the light rain in both direction between the airport and downtown. I picked a hotel that was only a couple blocks from a station, in this case Olive 8, and was happy with the experience.