We stayed at the Mayflower Park Hotel, which is in the city center, and convenient to all the main sights. The monorail to Seattle Center (Space Needle and Chilully Gardens) is right around the corner, and it's only a few blocks walk to Pike Market and the Waterfront. I am amazed at how much we could see in one day!
We took the Light Rail from the airport to Westgate Station, which is right by the hotel, and it was so easy and very inexpensive. There are other hotels in the Westgate area, but the Mayflower Park was the most reasonably priced - it is older, but still very nice, clean, safe and very friendly staff. The hotel offers a shuttle (for a fee) to the pier.