It was off the beach of Anse Lazio in the Seychelles where someone was taken by a shark, shame a poor honeymoon couple and they suspect it was the same shark that took the French tourist a few weeks before.
A shark attack in Zanzibar is unheard of, the beaches are protected by reefs which make the water too shallow most of the time for sharks.
Anyway Zanzibar is lovely and I think if you are wanting to stay somewhere like the Palms then you will be very happy. Tanzania and the people here are really amazing so doing a safari / beach option would be the best bet and I think it would save you a lot of time in terms of connections.
Some other good hotels to look at if you want a few options:
Anna of Zanzibar
Diamonds Star of the East
I think you will get a much more authentic African experience in Zanzibar. Stone Town is also a must in my opinion just for a night, I think it is such a great experience and lots of history and culture.