Freighthouse Square (http://freighthousesquare.com/) is a building three city blocks long, with shops and eating places inside, near the Tacoma Dome. Open M-Sa from 10AM-7PM and Sunday from noon to 5PM
The Tacoma Mall (http://simon.com/mall/def...), near Interstate 5 at the 38th Street exit is a major shopping center in Tacoma. A wide variety of stores extending well to the north and south of the mall, as well.