You will find some wonderful shopping in Hanoi. I recommend:
Craft Link, 41-43 Pho Van Mieu: This is a not-for-profit organization that buys good quality tribal handicrafts and weavings to fund community development for the artisans. You will find wonderful pillows, purses and scarves. I bought wonderful pillow covers which were very easy to bring home.
Hadong Silk, 102 Hang Gai: A lovely silk store in the Old Quarter.
Apricot Gallery, 40B Hang Bong Street: I like contemporary Vietnamese art and Apricot Gallery has wonderful artists and pieces. I found an artist, Bui Huu Hung, at their location in Saigon where I bought two large pieces.
Art Vietnam Gallery, 30 Hang Than St.: Very attractive gallery space with wonderful art.
Try to go to the studio of Mai Hien who does beautiful lacquer paintings.
Just outside the Old Quarter, my guide took me to Nghi Tam Street with many small antique shops. I loved exploring these stores and found some great finds.