Salt Cay isn't a major tourist destination and has a small number of tourists. As a result there is little shopping available on the island. There are only three local gift shops. 'Beachcombers - Unique Gifts from the Sea', which as the name suggests sells custom, one-of-a-kind souvenirs made form scavenged shells, floats and other items found washed ashore. This shop is located on the road to the airport and you can't miss it's distinctive sign. It's normally open form 2:00-5:00 PM, although it doesn't really have fixed hours.
Splash Boutique offers local artists a place to sell their handmade goods, such as sea glass and shell jewelry and paintings.
You can buy common food and grocery items (such as soft drinks, water, snacks, etc.) at the stores, but the selection is limited. Many of the local residents travel to Grand Turk once a week to get supplies. If you're staying for a while, buy any specialized items from Providenciales (or Grand Turk) before you travel.