Taking a "spice tour" on Zanzibar is kind of de rigueur. Shops and touts throughout Zanzibar's main city, Stone Town, will invite you to clamber into a vehicle and journey up the coast to see the farms that gave "The Island of Cloves" its name.
While this is informative and fun (and the tour companies usually also cook you a pretty decent seafood lunch), you can venture out to the coast on your own to get a look at seaweed farming. It's a smaller-scale venture than the spice plantations, but at low tide, you can wander among the seaweed farms themselves - stakes hammered into the sand with seaweed growing and curling around them.
Zanzibari women walk out to gather the kelp until the tide comes in again and the farms become inaccessible.