The streets are safe. Generally in Vedado you can drive around without any issues. Outside of the main city core, like in miramar or playa, it is fine to drive around.
The main issue for driving is in centro Habana or old Havana. You really should not be driving around there, in my opinion. In centro Habana everybody walks around in the street and the roads are in very bad condition. There is a lot of traffic. Even taxi drivers do not enjoy driving in centro Habana.
In old Havana, a lot of the area is closed to vehicle traffic. It is walking only. There are some parts of old Havana where you can drive, but the streets are very tight.
Overall, if you are just staying in Havana, you don’t need a car. It will be cheaper and more fun just to take taxis when you have to move around, or to walk.
Most people only rent cars when they have to travel to other cities in Cuba. But the highways are in poor condition and there are not many signs for directions. So even for that I would recommend just taking the taxis or buses.