I am keen car hirer when on holiday but don't bother in Zanzibar. You have to arrange a Zanzibari driving licence to drive on the island. Apparently most car rental agencies arrange this for you so is not much of a hassle.

In Nungwi you really dont need a car. You can walk everywhere. All hotels can arrange taxis and they aren't too expensive and are generally comfortable Toyota minivans with AC. You can befriend a taxi driver and do a deal privately if you want your own car and driver and just cut the hotel out of any commission if you want.

The roads on Zanzibar arent great (although better than a lot of Africa). There are lots of villages with policemen and speed bumps and signposting isnt great. The police are after bribes and not driving means you dont have to deal with that.

Is not too difficult to park in Stone Town but parking restrictions arent clear. You generally need to park outside the center and walk into the historic bit. A taxi will just drop off and collect you from the water front.

I have travelled round the whole island and prefer to just have a car and driver. Unless you plan on driving a lot you wont save much money self driving. Most tourist day trips will include transfers where they collect you from hotel. On Nungwi the beach is so nice you will probably want to relax there a few days.

If you want to explore the island best to book hotels in a few different areas and use taxis in between in my view.