If you step off the ferry in Stone Town and don't know anything about Zanzibar, the House of Wonders (or Beit al-Ajab, as it's also known) has you covered. Just a few steps away from the ferry terminal, you'll get a crash course in Swahili history.
The House was built by Sultan Barghash bin Said in 1883 and now that he's gone, it houses the Museum of History & Culture of Zanzibar & the Swahili Coast. The inner courtyard is the unlikely home to a huge Swahili sailing vessel and an old car that belonged Zanzibar's first president (didn't know Zanzibar had a president, other than the Tanzanian president? Yeah, neither did I. This is why you're in the right place to learn about these things.)
Despite the many cool - even, I daresay, wondrous - items in the museum, it was actually known as the House of Wonders because it was the first building in Zanzibar to boast electricity and the first building in East Africa to have an elevator.
Now that those things have become commonplace and boring, you can do a scavenger hunt through the building to find other wonders. Search for David Livingstone's medicine chest (let me just say - I do not think he ventured into central Africa adequately prepared), a Christmas-themed kanga, and a centuries-old charm that reportedly contains the nose of a dog.
As if that weren't enough, the gift shop is pretty well-stocked with interesting curios, too.