I love East Africa, but have it in the same bucket of ‘hard work for a holiday, but great experiences if you put the effort in’ of destinations I have countries like India in. I spent around 10 years flying to Tanzania, Kenya, Uganda and Zambia on a more or less weekly basis, so became well acquainted with the area. I visited Zanzibar once, and decided there were nicer and easier places to go the next times I went to Tanzania. It’s a very poor place, but beautiful. If you are interested in the history of Stonetown (primarily slavery related and really rather grim viewing,) are interested in the ecology of the area (there are a lot of conservation projects especially marine ones in the nearby islands) or are looking for a beach to relax on after safari in Tanzania, then yes, I can very much recommend it. If you are hoping for an exotic beach getaway I could recommend any other number of destinations. Zanzibar is not easy to get to, and doesn’t really have a very established AI industry. It’s a long difficult way to go just for a bit of beach.
Regarding health, the East coast of Africa was one of the highest risk areas I have been to in my line of work (aviation.) Tanzania and neighbouring Uganda were the only places we were given malaria prophylaxis if we spent time outside of the air conditioned crew hotels. The whole of Tanzania (except for the tops of mountains) is high risk for malaria. There has been a WHO drive to reduce malaria transmission in Zanzibar itself, but it has not been fully successful and there has been a rise in the immediate past in cases of malaria in travellers returning from Zanzibar. You will definitely need malaria tablets, Malarone is what they used to give us.
You will also need to go to a travel clinic who can give you the best advice for vaccinations, however you will probably need all your standard childhood jabs to be present, with boosters for some (eg tetanus and polio,) and new vaccinations for things such as cholera, hepatitis A&B, and typhoid.
Also be aware of the fact that you will want to be using the most effective insect repellent you can lay your hands on - there are many more insect-borne diseases out there than you may have imagined. Dengue, chikunyunga, zika, leishmaniasis, schistosomiasis, and a whole raft of other fly, mosquito, tick and even snail transmitted diseases. 50% DEET applied hourly is your best defence here.
For all of the reasons above, when the children were small and I had the opportunity to take them with me to work I decided not to take them here. I took them to the Bahamas instead (it was the only other beach destination I worked to at the time. Not sure I’d recommend the Bahamas for a holiday either! But I am picky! 🤣) I took my DH, mum and brother though, and had wonderful trips. I did not get ill, but I’m vaccinated to the eyeballs as a result of all the destinations I visit, and get unlimited free DEET and Malarone through work. I also have a digestive system used to different influences, and a well-drilled in sense of personal hygiene that comes from the knowledge that eg paper money is a great store of bacteria, so wash your hands after handling it and before eating, and tops of cans and bottles are not great for drinking out of - there may have been rats in the storage area climbing on them, use a straw or a glass.
If you are still set on Zanzibar, have fun. The beaches and the sea life are stunning and the people among the friendliest in East Africa. You should definitely make the effort to stay on mainland Tanzania too though and go on a safari.