Macy's and Nordstroms. As well as some discount shops like Nordstrom Rack. Or you can find some nice boutiques that are unique to Seattle.
Westlake Center and most of the popular shops are either inside or close by to this mall. If you want to experience eating in the mall Food Court you can go to the top floor of Westlake Center. But, if you want to eat good food I recommend you find a restaurant or cafe outside of the mall.
I hope you have a chance to visit Seattle or that I at least was able to give you a nice glimpse into this wonderful city. It will always be one of my favorite cities!