Here is a map to give you an idea of where things are that I have done and distances.
From Zanzibar town to the Tunguu campus every morning and afternoon is a 30 minute drive each way. When we went to the beach at Pwani Mchangani, we drove for about an hour. I saw signs that indicated it was about 30-35 kilometers from Stone Town or 18-20 miles. Given the roads and the towns we passed through, that seems right.
The market area is about 10 minute walk and the restaurants with the sunset view are about 15 minutes. There are a few closer, but I usually go down closer to the Shangani area. If I walk from my place, it is about a 5 minute walk to the Ferry terminal where you can take the ferry to Dar es Salaam. It is approximately where it says wharf on the map. All of the faculty and staff that I have met live in the Stone Town area, many in the Vuga area that directly south and inland from the sunset views near the roundabout (rotary) that is south of my sunset view circle. I learned that that area used to separated by a large creek/river from the other part of Zanzibar. The Vuga area was originally where the Western settlers and diplomats lives and the locals only came over by boat each day to work for the elite. Now, many people live in the Vuga area are they have filled in the creek so it is all solid land, similar to the situation of Boston.
Here is a website with a driving video and history for those who are interested. The top is a set of key dates, but scroll down for more in-depth information.