Newbury Street in the Back Bay is the city's flagship shopping street — eight blocks of nineteenth-century brownstones converted to boutiques, with prices climbing as you move east toward the Public Garden. Copley Place and the Prudential Center, both indoor malls connected by skybridge, handle the chains and luxury brands.
For more interesting shopping, head to Charles Street on Beacon Hill (antiques, independent bookshops, gourmet food), Harvard Square across the river in Cambridge (used books, vintage clothes, university gear), or the SoWa Sunday market in the South End (vintage, art, food trucks; May through October). Quincy Market at Faneuil Hall is geared squarely at tourists and best avoided unless you specifically want a Boston hoodie.
For one truly special stop, the Brattle Book Shop downtown — open since 1825 — is one of the oldest used bookshops in the country and worth a browse.