The following hotels are within walking distance (less than 1/4 mile) and I am sure they all have shuttle buses too:

Doubletree Seatac Airport
Wyndham Hotel
West Coast hotels (2)

These are the easiest to get to and the closest, and walking is not a problem, there are sidewalks and cross walks and it is safe even at 5 am. Cost I am not so sure about. My choice would be the Doubletree (former Red Lion) but I don't know how much you want to spend for a few hours sleep.