Nungwi beach is located at the northern tip of Zanzibar and has over 20 dive spots and some really wonderful beach areas for relaxing. Nungwi itself is a village that has been famous for its shipbuilding (the ever-present dhows) for over 500 years. The fish auction on the beach is open to all who want to come by to purchase or just look on. I'd also suggest a visit to the lighthouse where there's a small aquarium filled with turtles. The variety of restaurants and bars offering affordable local food is outstanding.
The official language of Nungwi is Swahili and I'd recommend visiting the town to check out the tropical fruit markets and the local schools.