Unless you are planning on staying with a family in the absolute ends of the city, a car would be way more hassel than it's worth. Traffic in the city, especially to any place you'd want to go, is monsterous, parking is expensive, and Turkish driving is an art that takes a lot of time to master. That, of course, is a polite way to say that people drive like maniacs here and do not obey any conventional rules of the road.
Realistically, as a tourist, any place you'd like to get to is close to public transport, although some destinations, like Bebek or Arnavutkoy, will be a bit of a slog. More to the point, walk as much as you can in the city- I find it really really really rewards you for exploring it on foot, and it's nice to be able to get a little bit lost.
