With a sim card bought at airport and a data plan, you can navigate the island easily just using Google maps. Stone Town is not very big and is not that hard to navigate. Yes some streets are a bit narrow. I wouldn't be very concerned about car crime but obviously don't leave valuables visible when car is unattended.

Drivers in Stone Town and the across the island are not aggressive and there isn't much speeding due to lots of police and cameras about. Avoid driving at night due to lack of street lights and people and livestock in street/road.

The roads aren't great and there are pot holes and lots of tracks as well as a few hard to spot speed bumps. If you can stretch to a 4x4 would be more comfortable but unnecessary in terms of need for off road capability.

To be honest though unless you are going to make good use of the car, I would just use taxis. They are easy to arrange and drivers (like all Zanzibaris in general) are very friendly and helpful. You can then make trips back to hotel from beaches after sunsets (and possibly a few drinks) without the hassle of driving. Parking in Stone Town can occasionally also be a bit of a pain. Taxis get rid of this hassle too.