Castries market is a good place to buy gifts as is the JQ Shopping Mall in Rodney Bay. There is also La Place Carenage, a duty free and gift and souvenir outlet located in the main harbour of Castries. There you will find fine jewellry arts and crafts, ideal for gifts.
Supermarkets have quite good prices on rums produced or bottled on the island, e.g., Elements 8, Admiral Rodney, and especially Chairman's Reserve.
Visits by cruise ships over the years have generated a duty free mall (at dockside, Point Seraphine, Castries) with jewelry, souvenirs, art, liquor/rums and other offerings typical for cruise shoppers.
You may also find lower, "duty-Free" prices available across the island in strip malls and resortts. You may need identification as a visitor to qualify for duty-free treatment.