There's plenty to do. The express bus will take you to the Westin.
1) Visit the downtown shopping district, Nordstrom, Bon marche, Pacific Place Mall, Westlake Center Mall, boutique stores on 5th Ave.
2) Go to Pike Place Market
3) Take a ferry ride or tour of Elliott bay down at the waterfront.
For dinner there are a huge number of great restaurants in Seattle. In acy case it sure beats hanging out at the airport.