Antigua is home to a wide variety of shops and boutiques, selling everything from handmade Antiguan gifts and cool Caribbean clothing to duty-free perfumes, watches, and crystal. Heritage Quay in St. John's is the place for duty-free (there is even a casino here), while Redcliffe Quay has some nice shops with a more authentic West Indian feel.
You won't want to miss a visit to the Heritage Market in St. John's. Come on a Saturday morning if possible. The market is located across from the West Street Bus Station and opens early (around 5:30 AM). Here you will find plenty of locally-grown produce, and the vendors will be happy to fill you in on anything you don't recognize. There's also a small arts and crafts market attached to the main market.
Store hours vary, but the majority are open from 8:30-12:00 and 1:00-5:00 Monday to Saturday. Shops stay open longer when cruise ships are in port. Be sure to stick around your Antigua villas on Sunday - shops are open Monday through Saturday only!