Take the buses up the hills! It’s really easy to do.
you may have to wait a little longer for buses on the weekends, but honestly, in the “core” you don’t have to wait long, 15 minutes tops.
The bus you will want to take from the Westin up the Asian Art Museum is the number 10.
For an example, go here – http://tripplanner.metrokc.gov/cgi-bin/itin_page.pl?resptype=U – and enter
Westin Hotel (as the starting point)
Seattle Asian Art Museum (as the ending point.