The waterfront along Veterans Drive in Charlotte Amalie has a string of restaurants ranging from open-air conch shacks to more polished dining rooms overlooking the harbour. The best of them lean into local ingredients: fresh fish, conch fritters, pates (pronounced pah-tays, the local fried dough pockets filled with saltfish, beef, or vegetables), and johnnycake. Kallaloo, a leafy stew with okra and seafood, turns up on menus that make an effort to go beyond generic Caribbean food.
For a more local experience, the covered market on the waterfront and the streets behind Main Street are where you'll find the roti stands and family-run lunch spots that cater to residents rather than cruise ship passengers. The food is cheaper and more interesting: goat stew, fish and fungi (a cornmeal dish that is the unofficial national side), and fresh fruit from the market stalls.
A word of timing: many restaurants in Charlotte Amalie close or scale back on evenings when the cruise ships have left, since the lunch trade is where the money is. If you want dinner, the Frenchtown neighbourhood just west of the cruise ship terminal (an enclave settled by French-speaking migrants from St. Barts and St. Martin in the 19th century) has a cluster of restaurants that stay open into the evening and cater more to residents and hotel guests.